O. Devauchelle, E. Lajeunesse, F. James, C. Josserand, P. Lagrée
Couder et al. [1] discovered that the behavior of droplets bouncing on a vibrated bath mimics a variety of quantum phenomena, through their coupling with a Faraday wave. Here, we introduce a continuous model inspired from this experiment, which encapsulates its essential features into a system of three simple differential equations. We show, numerically and analytically, the existence of self-propelled walkers in this framework. Finally, making use of the model’s familiar formulation, we suggest that a particle coupled with a propagating wave, instead of a standing one, behaves much like a bouncing droplet.
{"title":"Walkers in a wave field with memory","authors":"O. Devauchelle, E. Lajeunesse, F. James, C. Josserand, P. Lagrée","doi":"10.5802/crmeca.29","DOIUrl":"https://doi.org/10.5802/crmeca.29","url":null,"abstract":"Couder et al. [1] discovered that the behavior of droplets bouncing on a vibrated bath mimics a variety of quantum phenomena, through their coupling with a Faraday wave. Here, we introduce a continuous model inspired from this experiment, which encapsulates its essential features into a system of three simple differential equations. We show, numerically and analytically, the existence of self-propelled walkers in this framework. Finally, making use of the model’s familiar formulation, we suggest that a particle coupled with a propagating wave, instead of a standing one, behaves much like a bouncing droplet.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"163 1","pages":"591-611"},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76637529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neutral modes related to spontaneous broken symmetries at the onset of a pattern-forming instability can strongly modify the nature of secondary instabilities of the pattern. In particular these neutral modes can change the order of the secondary transition making it first order or subcritical in the language of bifurcation theory. We first discuss this phenomenon in the context of the drift bifurcation from stationary to traveling patterns. We then consider patterns that undergo a spatial period-doubling bifurcation like the Peierls transition in solid state physics. Résumé. Je rappelle comment une expérience réalisée par Yves Couder et son groupe a motivé des travaux théoriques qui ont montré que les modes de phase d’une structure cellulaire engendrée par instabilité peuvent affecter la nature des instabilités secondaires de cette structure, à savoir, le caractère propagatif ou non de l’instabilité secondaire et sa sous-criticalité. Je discute ensuite la sous-criticalité résultant du couplage avec les modes de phase sur d’autres exemples tels que la transition de Peierls en physique de la matière condensée.
中性时尚related to a破symmetries at the onset of spontaneous pattern-forming adc instability,从与the nature of中学触发圣母的模式。In these中性方式具有法律地位的can change the order of the making it first order or中学过渡subcritical In the language of分叉理论。= =地理= =根据美国人口普查，这个县的面积为。We then that年联同形态空间一下了分叉period-doubling like the Peierls转变in solid state物理学。摘要。提醒我怎么Yves Couder和他的团队所做的一项实验,已促使显示模式的理论研究阶段的细胞结构所引发的动荡可能影响次要性质不稳定的这种结构,即是否是propagatif中学和其sous-criticalité动荡。然后，我将在凝聚态物理中的Peierls跃迁等例子中讨论由相模耦合引起的次临界性。
{"title":"Effect of neutral modes on the order of a transition","authors":"S. Fauve","doi":"10.5802/crmeca.21","DOIUrl":"https://doi.org/10.5802/crmeca.21","url":null,"abstract":"Neutral modes related to spontaneous broken symmetries at the onset of a pattern-forming instability can strongly modify the nature of secondary instabilities of the pattern. In particular these neutral modes can change the order of the secondary transition making it first order or subcritical in the language of bifurcation theory. We first discuss this phenomenon in the context of the drift bifurcation from stationary to traveling patterns. We then consider patterns that undergo a spatial period-doubling bifurcation like the Peierls transition in solid state physics. Résumé. Je rappelle comment une expérience réalisée par Yves Couder et son groupe a motivé des travaux théoriques qui ont montré que les modes de phase d’une structure cellulaire engendrée par instabilité peuvent affecter la nature des instabilités secondaires de cette structure, à savoir, le caractère propagatif ou non de l’instabilité secondaire et sa sous-criticalité. Je discute ensuite la sous-criticalité résultant du couplage avec les modes de phase sur d’autres exemples tels que la transition de Peierls en physique de la matière condensée.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"44 1","pages":"475-487"},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80263838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
At the beginning of the eighties Yves Couder started to work in pattern formation field trying to observe and understand structures in complex flows. His approach was different using humble experiments to materialise simple but powerful and elegant ideas. He was establishing with Pierre Gilles De Gennes and Étienne Guyon in particular a novel way of making scientific proof by using demystified “experiences de coin de table” where the simplicity of the setting made the demonstration even more powerful. Science was becoming performative and scientists were in public talks as well as in the lab engaged physically in a tactile way with their experiments. One of Yves first contributions was to use soap films to perform hydrodynamics experiments in two dimensions. The experiments with soap films brought a sense of fragility, emotion and poetry into science; they started and entirely new field of research on bidimensional turbulence using films. This research and novel approach to science opened a pathway for some current domains like table-top sciences, frugal sciences, new types of popularisation like “la main à la pate”, but also the rapidly developing field of arts & sciences. In the present article I will draw on the affiliation of Yves’ works with the arts and sciences using several examples from my own work which is greatly inspired by his approach but also from the work of the fantastic artist duo Evelina Domnitch and Dmitry Gelfand.
20世纪80年代初，伊夫·库德开始在模式形成领域工作，试图观察和理解复杂流动中的结构。他的方法是不同的，用简单的实验来实现简单但强大而优雅的想法。他与Pierre Gilles De Gennes和Étienne Guyon一起建立了一种新颖的科学证明方式，通过使用去神秘化的“经验，硬币，桌子”，简单的设置使演示更加强大。科学变得越来越具有表演性，科学家们不仅在实验室里做实验，也在公开场合做演讲。伊夫最早的贡献之一是利用肥皂膜进行二维流体力学实验。肥皂片的实验给科学带来了脆弱、情感和诗意;他们开创了利用薄膜研究二维湍流的全新领域。这项研究和新颖的科学方法为一些当前的领域开辟了一条道路，如桌面科学，节俭科学，新型的普及，如“主流科学”，以及快速发展的艺术和科学领域。在这篇文章中，我将利用我自己的作品中的几个例子来借鉴伊夫的作品与艺术和科学的联系，我的作品深受他的方法的启发，也受到了出色的艺术家二人组Evelina Domnitch和Dmitry Gelfand的作品的启发。
{"title":"Terra Bulla, the influence of Yves Couder on the emerging domain of arts and physics sciences","authors":"J. Chomaz","doi":"10.5802/crmeca.20","DOIUrl":"https://doi.org/10.5802/crmeca.20","url":null,"abstract":"At the beginning of the eighties Yves Couder started to work in pattern formation field trying to observe and understand structures in complex flows. His approach was different using humble experiments to materialise simple but powerful and elegant ideas. He was establishing with Pierre Gilles De Gennes and Étienne Guyon in particular a novel way of making scientific proof by using demystified “experiences de coin de table” where the simplicity of the setting made the demonstration even more powerful. Science was becoming performative and scientists were in public talks as well as in the lab engaged physically in a tactile way with their experiments. One of Yves first contributions was to use soap films to perform hydrodynamics experiments in two dimensions. The experiments with soap films brought a sense of fragility, emotion and poetry into science; they started and entirely new field of research on bidimensional turbulence using films. This research and novel approach to science opened a pathway for some current domains like table-top sciences, frugal sciences, new types of popularisation like “la main à la pate”, but also the rapidly developing field of arts & sciences. In the present article I will draw on the affiliation of Yves’ works with the arts and sciences using several examples from my own work which is greatly inspired by his approach but also from the work of the fantastic artist duo Evelina Domnitch and Dmitry Gelfand.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"7 1","pages":"447-456"},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91045046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tribute to an exemplary man: Yves Couder","authors":"M. B. Amar, L. Limat, O. Pouliquen, E. Villermaux","doi":"10.5802/crmeca.35","DOIUrl":"https://doi.org/10.5802/crmeca.35","url":null,"abstract":"","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"11 1","pages":"393-395"},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75325145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We revisit de Broglie’s double-solution pilot-wave theory in light of insights gained from the hydrodynamic pilot-wave system discovered by Couder and Fort [1]. de Broglie proposed that quantum particles are characterized by an internal oscillation at the Compton frequency, at which rest mass energy is exchanged with field energy. He further proposed that the resulting pilot-wave field satisfies the Klein–Gordon equation. While he developed a guidance equation for the particle, he did not specify how the particle generates the wave. Informed by the hydrodynamic pilot-wave system, we explore a variant of de Broglie’s mechanics in which the form of the Compton-scale dynamic interaction between particle and pilot wave is specified. The particle is modeled as a localized periodic disturbance of the Klein–Gordon field at twice the Compton frequency. We simulate the evolution of the particle position by assuming that the particle is propelled by the local gradient of its pilot wave field. Resonance is achieved between the particle and its pilot wave, leading to self-excited motion of the particle. The particle locks into quasi-steady motion characterized by a mean momentum p̄ =ħk, where k is the wavenumber of the surrounding matter waves. Speed modulations along the particle path arise with the de Broglie wavelength and frequency ck. The emergent dynamics is strongly reminiscent of that arising in the hydrodynamic pilot-wave system, on the basis of which we anticipate the emergence of quantum statistics in various settings. Our results suggest the potential value of a new hydrodynamically-inspired pilot-wave theory for the motion of quantum particles.
{"title":"Hydrodynamic quantum field theory: the free particle","authors":"Y. Dagan, J. M. Bush","doi":"10.5802/crmeca.34","DOIUrl":"https://doi.org/10.5802/crmeca.34","url":null,"abstract":"We revisit de Broglie’s double-solution pilot-wave theory in light of insights gained from the hydrodynamic pilot-wave system discovered by Couder and Fort [1]. de Broglie proposed that quantum particles are characterized by an internal oscillation at the Compton frequency, at which rest mass energy is exchanged with field energy. He further proposed that the resulting pilot-wave field satisfies the Klein–Gordon equation. While he developed a guidance equation for the particle, he did not specify how the particle generates the wave. Informed by the hydrodynamic pilot-wave system, we explore a variant of de Broglie’s mechanics in which the form of the Compton-scale dynamic interaction between particle and pilot wave is specified. The particle is modeled as a localized periodic disturbance of the Klein–Gordon field at twice the Compton frequency. We simulate the evolution of the particle position by assuming that the particle is propelled by the local gradient of its pilot wave field. Resonance is achieved between the particle and its pilot wave, leading to self-excited motion of the particle. The particle locks into quasi-steady motion characterized by a mean momentum p̄ =ħk, where k is the wavenumber of the surrounding matter waves. Speed modulations along the particle path arise with the de Broglie wavelength and frequency ck. The emergent dynamics is strongly reminiscent of that arising in the hydrodynamic pilot-wave system, on the basis of which we anticipate the emergence of quantum statistics in various settings. Our results suggest the potential value of a new hydrodynamically-inspired pilot-wave theory for the motion of quantum particles.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"113 1","pages":"555-571"},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86022429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a pioneering series of experiments, Yves Couder, Emmanuel Fort and coworkers demonstrated that droplets bouncing on the surface of a vertically vibrating fluid bath exhibit phenomena reminiscent of those observed in the microscopic quantum realm. Inspired by this discovery, we here conduct a theoretical and numerical investigation into the structure and dynamics of one-dimensional chains of bouncing droplets. We demonstrate that such chains undergo an oscillatory instability as the system’s wave-induced memory is increased progressively. The predicted oscillation frequency compares well with previously reported experimental data. We then investigate the resonant oscillations excited in the chain when the drop at one end is subjected to periodic forcing in the horizontal direction. At relatively high memory, the drops may oscillate with an amplitude larger than that prescribed, suggesting that the drops eVectively extract energy from the collective wave field. We also find that dynamic stabilization of new bouncing states can be achieved by forcing the chain at high frequency. Generally, our work provides insight into the collective behavior of particles interacting through long-range and temporally nonlocal forces.
{"title":"Resonant interactions in bouncing droplet chains","authors":"Lauren Barnes, G. Pucci, Anand U. Oza","doi":"10.5802/crmeca.30","DOIUrl":"https://doi.org/10.5802/crmeca.30","url":null,"abstract":"In a pioneering series of experiments, Yves Couder, Emmanuel Fort and coworkers demonstrated that droplets bouncing on the surface of a vertically vibrating fluid bath exhibit phenomena reminiscent of those observed in the microscopic quantum realm. Inspired by this discovery, we here conduct a theoretical and numerical investigation into the structure and dynamics of one-dimensional chains of bouncing droplets. We demonstrate that such chains undergo an oscillatory instability as the system’s wave-induced memory is increased progressively. The predicted oscillation frequency compares well with previously reported experimental data. We then investigate the resonant oscillations excited in the chain when the drop at one end is subjected to periodic forcing in the horizontal direction. At relatively high memory, the drops may oscillate with an amplitude larger than that prescribed, suggesting that the drops eVectively extract energy from the collective wave field. We also find that dynamic stabilization of new bouncing states can be achieved by forcing the chain at high frequency. Generally, our work provides insight into the collective behavior of particles interacting through long-range and temporally nonlocal forces.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"50 4 1","pages":"573-589"},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86068053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
O. Cadot, Maha Almarzooqi, Antoine Legeai, V. Parezanović, L. Pastur
The paper reports on the bi-stable turbulent wake dynamics of a three-dimensional bluff body. It is shown that the occurrence of the switching between the two wake states decreases as the turbulent intensity of the incoming flow is made larger by an additional upstream grid. A detailed analysis of the jumps statistics indicates that the turbulent fluctuation of each wake state is also decreased. It is concluded that the states switching is thus triggered by large fluctuations produced by the wake instabilities and not by those of the incoming flow. It is also shown that increasing the free-stream turbulence intensity reinforces the permanent asymmetry of each state and increases the wake sensitivity to residual asymmetries.
{"title":"On three-dimensional bluff body wake symmetry breaking with free-stream turbulence and residual asymmetry","authors":"O. Cadot, Maha Almarzooqi, Antoine Legeai, V. Parezanović, L. Pastur","doi":"10.5802/crmeca.32","DOIUrl":"https://doi.org/10.5802/crmeca.32","url":null,"abstract":"The paper reports on the bi-stable turbulent wake dynamics of a three-dimensional bluff body. It is shown that the occurrence of the switching between the two wake states decreases as the turbulent intensity of the incoming flow is made larger by an additional upstream grid. A detailed analysis of the jumps statistics indicates that the turbulent fluctuation of each wake state is also decreased. It is concluded that the states switching is thus triggered by large fluctuations produced by the wake instabilities and not by those of the incoming flow. It is also shown that increasing the free-stream turbulence intensity reinforces the permanent asymmetry of each state and increases the wake sensitivity to residual asymmetries.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"209 1","pages":"509-517"},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74602497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A toroidal bubble or a cylindrical gas jet are known to be subjected to the Rayleigh-Plateau instability. Air bubble rings produced by beluga whales and dolphins however are observed that remain stable for long times. In the present work, we analyse the generation of such toroidal bubbles via numerical simulations , in particular how the process depends on surface tension. Their stability properties are then briefly analysed. For the estimated Reynolds and Weber numbers relative to the bubbles produced by these animals, the presence of a vortex inside and around the bubble is found to strongly stabilize the Rayleigh-Plateau instability .
{"title":"Instability of a swirling bubble ring","authors":"Yonghui Xu, I. Delbende, D. Fuster, M. Rossi","doi":"10.5802/crmeca.22","DOIUrl":"https://doi.org/10.5802/crmeca.22","url":null,"abstract":"A toroidal bubble or a cylindrical gas jet are known to be subjected to the Rayleigh-Plateau instability. Air bubble rings produced by beluga whales and dolphins however are observed that remain stable for long times. In the present work, we analyse the generation of such toroidal bubbles via numerical simulations , in particular how the process depends on surface tension. Their stability properties are then briefly analysed. For the estimated Reynolds and Weber numbers relative to the bubbles produced by these animals, the presence of a vortex inside and around the bubble is found to strongly stabilize the Rayleigh-Plateau instability .","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"67 1","pages":"519-535"},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76306470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, I briefly discuss the remarkable scientific accomplishments of Yves Couder, their impact in the fluid dynamics community worldwide and his unique personality. It is a personal tribute to a friend and a colleague I have known for the past 35 years.
{"title":"Yves Couder (1941–2019): A life in search of the beauty of fluid motion","authors":"P. Huerre","doi":"10.5802/crmeca.37","DOIUrl":"https://doi.org/10.5802/crmeca.37","url":null,"abstract":"In this article, I briefly discuss the remarkable scientific accomplishments of Yves Couder, their impact in the fluid dynamics community worldwide and his unique personality. It is a personal tribute to a friend and a colleague I have known for the past 35 years.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"35 1","pages":"397-400"},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77208979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper deals with the numerical computation of difficult problems requiring many steps and many degrees of freedom such as the finite element analysis of wrinkling of film–substrate systems. The asymptotic numerical method (ANM) is well adapted to such computations but with a progressive loss of accuracy during step chaining. Thus, correction phases are necessary, which are rarely carried out within ANM. A convergence acceleration algorithm and a step-length adaptation have been included to limit the growth of computation time and to strengthen the reliability of the procedure. This modified version of the ANM is assessed by simulating the appearance and evolution of sinusoidal wrinkles under uniaxial compression. Résumé. L’article étudie le calcul numérique de problèmes difficiles nécessitant de nombreux pas et un grand nombre de degrés de liberté, comme l’étude par éléments finis du plissement de systèmes film– substrat. La méthode asymptotique numérique (ANM) est bien adaptée à de tels calculs, mais avec une lente perte de précision lors de l’enchainement de nombreux pas de calculs. Donc des étapes de correction sont indispensables, ce qui est rarement fait lors de calculs par ANM. L’algorithme de cheminement est complété par une méthode d’accélération de convergence et par une technique d’adaptation de la longueur de pas pour minimiser le temps de calcul et pour fiabiliser la procédure. Cette version modifiée de la méthode asymptotique numérique a été évaluée par la simulation de l’apparition de plis sinusoïdaux en compression
本文讨论了薄膜-衬底系统起皱的有限元分析等多步骤、多自由度难题的数值计算。渐近数值方法(ANM)可以很好地适应这种计算，但在步进链过程中精度会逐渐下降。因此，修正阶段是必要的，这在ANM中很少执行。为了限制计算时间的增长和增强程序的可靠性，采用了收敛加速算法和步长自适应算法。通过模拟单轴压缩下正弦褶皱的外观和演变来评估这种改进版的ANM。的简历。第1条:计算有问题的、有困难的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的。“无渐进式”(ANM)与“无渐进式”(ANM)相适应，“无渐进式”(ANM)与“无渐进式”(ANM)相适应，与“无渐进式”(ANM)相适应。唐认为，调校是不可缺少的，因为调校过程中出现了大量的错误，这与ANM的计算是一致的。L 'algorithme de cheminement est完成相当一个方法d 'acceleration de收敛等par 'adaptation de la小说德不是一个技术将自动喷雾器le temps计算等倒fiabiliser la过程。Cette版本修改了simacrique和simacrique的渐进式simacrique和simacrique的simacrique和simacrique的simacrique的模拟de '幻影de plis sinusoïdaux en压缩
{"title":"A secure version of asymptotic numerical method via convergence acceleration","authors":"P. Ventura, M. Potier-Ferry, H. Zahrouni","doi":"10.5802/crmeca.48","DOIUrl":"https://doi.org/10.5802/crmeca.48","url":null,"abstract":"The paper deals with the numerical computation of difficult problems requiring many steps and many degrees of freedom such as the finite element analysis of wrinkling of film–substrate systems. The asymptotic numerical method (ANM) is well adapted to such computations but with a progressive loss of accuracy during step chaining. Thus, correction phases are necessary, which are rarely carried out within ANM. A convergence acceleration algorithm and a step-length adaptation have been included to limit the growth of computation time and to strengthen the reliability of the procedure. This modified version of the ANM is assessed by simulating the appearance and evolution of sinusoidal wrinkles under uniaxial compression. Résumé. L’article étudie le calcul numérique de problèmes difficiles nécessitant de nombreux pas et un grand nombre de degrés de liberté, comme l’étude par éléments finis du plissement de systèmes film– substrat. La méthode asymptotique numérique (ANM) est bien adaptée à de tels calculs, mais avec une lente perte de précision lors de l’enchainement de nombreux pas de calculs. Donc des étapes de correction sont indispensables, ce qui est rarement fait lors de calculs par ANM. L’algorithme de cheminement est complété par une méthode d’accélération de convergence et par une technique d’adaptation de la longueur de pas pour minimiser le temps de calcul et pour fiabiliser la procédure. Cette version modifiée de la méthode asymptotique numérique a été évaluée par la simulation de l’apparition de plis sinusoïdaux en compression","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"25 1","pages":"361-374"},"PeriodicalIF":0.8,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84393555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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