Polymers are known to degrade in their use conditions, with the risk that their properties reach unacceptable level. This paper reviews the modeling of modifications occurring at molecular and architectural changes occurring during their chemical ageing, with the aim of predicting the physical (mechanical) properties, all values being linked by structure properties relationships.
{"title":"Physico-chemical approach of polymer chemical ageing: a short review","authors":"E. Richaud","doi":"10.5802/crmeca.64","DOIUrl":"https://doi.org/10.5802/crmeca.64","url":null,"abstract":"Polymers are known to degrade in their use conditions, with the risk that their properties reach unacceptable level. This paper reviews the modeling of modifications occurring at molecular and architectural changes occurring during their chemical ageing, with the aim of predicting the physical (mechanical) properties, all values being linked by structure properties relationships.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87977224","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}
Y. Charles, Chun-Lei Zhang, M. Gaspérini, B. Bacroix
The present paper deals with the consideration of the rate-sensitivity mechanical behavior of metallic materials, in the framework of mean field and full field homogenization approaches. We re-examine the possibility of describing properly this rate sensitivity with a simple and widely used power law expressed at the level of the slip system, and we propose a methodology to accelerate the identification of the global material constitutive law for Finite Element (FE) simulations. For such an aim, simulations of a tensile test are conducted, using a simple homogenization model (the Taylor one, used in a relaxed constraint form) and an FE code (Abaqus), both using the same single-crystal rate-dependent constitutive law. It is shown that, provided that the identification of this law is performed with care and well adapted to the examined case (rate-sensitive or insensitive materials, static and/or dynamic ranges), the simple power law can be used to simulate the macroscopic behavior of polycrystalline aggregates in a wide range of strain rate (including both static and dynamic regimes) and strain-rate sensitivity values (up the rate-insensitive limit).
{"title":"Identification methodology of a rate-sensitive constitutive law with mean field and full field modeling approaches for polycrystalline materials","authors":"Y. Charles, Chun-Lei Zhang, M. Gaspérini, B. Bacroix","doi":"10.5802/crmeca.56","DOIUrl":"https://doi.org/10.5802/crmeca.56","url":null,"abstract":"The present paper deals with the consideration of the rate-sensitivity mechanical behavior of metallic materials, in the framework of mean field and full field homogenization approaches. We re-examine the possibility of describing properly this rate sensitivity with a simple and widely used power law expressed at the level of the slip system, and we propose a methodology to accelerate the identification of the global material constitutive law for Finite Element (FE) simulations. For such an aim, simulations of a tensile test are conducted, using a simple homogenization model (the Taylor one, used in a relaxed constraint form) and an FE code (Abaqus), both using the same single-crystal rate-dependent constitutive law. It is shown that, provided that the identification of this law is performed with care and well adapted to the examined case (rate-sensitive or insensitive materials, static and/or dynamic ranges), the simple power law can be used to simulate the macroscopic behavior of polycrystalline aggregates in a wide range of strain rate (including both static and dynamic regimes) and strain-rate sensitivity values (up the rate-insensitive limit).","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72837147","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 self-consistent (SC) theory is the most commonly used mean-field homogenization method to estimate the mechanical response behavior of polycrystals based on the knowledge of the properties and orientation distribution of constituent single-crystal grains. The original elastic SC method can be extended to thermo-elasticity by adding a stress-free strain to an elastic constitutive relation that expresses stress as a linear function of strain. With the addition of this independent term, the problem remains linear. Although the thermo-elastic self-consistent (TESC) model has important theoretical implications for the development of self-consistent homogenization of non-linear polycrystals, in this paper, we focus on TESC applications to actual thermo-elastic problems involving non-cubic (i.e. thermally anisotropic) materials. To achieve this aim, we provide a thorough description of the TESC theory, which is followed by illustrative examples involving cooling of polycrystalline non-cubic metals. The TESC model allows studying the effect of crystallographic texture and single-crystal elastic and thermal anisotropy on the effective thermo-elastic response of the aggregate and on the internal stresses that develop at the local level.
{"title":"Polycrystal thermo-elasticity revisited: theory and applications","authors":"C. Tomé, R. Lebensohn","doi":"10.5802/crmeca.18","DOIUrl":"https://doi.org/10.5802/crmeca.18","url":null,"abstract":"The self-consistent (SC) theory is the most commonly used mean-field homogenization method to estimate the mechanical response behavior of polycrystals based on the knowledge of the properties and orientation distribution of constituent single-crystal grains. The original elastic SC method can be extended to thermo-elasticity by adding a stress-free strain to an elastic constitutive relation that expresses stress as a linear function of strain. With the addition of this independent term, the problem remains linear. Although the thermo-elastic self-consistent (TESC) model has important theoretical implications for the development of self-consistent homogenization of non-linear polycrystals, in this paper, we focus on TESC applications to actual thermo-elastic problems involving non-cubic (i.e. thermally anisotropic) materials. To achieve this aim, we provide a thorough description of the TESC theory, which is followed by illustrative examples involving cooling of polycrystalline non-cubic metals. The TESC model allows studying the effect of crystallographic texture and single-crystal elastic and thermal anisotropy on the effective thermo-elastic response of the aggregate and on the internal stresses that develop at the local level.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84718259","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 present work demonstrates that the pencil glide mechanism is a physically reliable and a computationally efficient model to simulate the nonlinear behaviour of b.c.c. single and polycrystals. For that purpose, the pencil glide extension of Schmid’s criterion used by Gilormini [1] is incorporated in a single crystal model and in a homogenized polycrystal model accounting for large elastoviscoplastic deformations. The response of the pencil glide model in terms of stress-strain curves and lattice rotation is compared to the prediction based on the consideration of all ({110}〈111〉+ {112}〈111〉) slip systems. In the case of α-iron single crystals both approaches are shown to accurately reproduce recent experimental results [2, 3]. The comparison is extended to α-iron polycrystals behaviour under tension, compression, rolling and simple shear loading conditions. The evolution of crystallographic textures obtained either based on pencil glide or using the 24 slip systems is analyzed and compared to classical experimental results from the literature. Limitations of the approach, especially in the case of simple shear textures, are also pointed out. The pencil glide approach can be viewed as a reduced order model enhancing computational efficiency of crystal plasticity simulations involving many slip mechanisms.
{"title":"Efficient simulation of single and poly-crystal plasticity based on the pencil glide mechanism","authors":"L. T. Le, K. Ammar, S. Forest","doi":"10.5802/crmeca.44","DOIUrl":"https://doi.org/10.5802/crmeca.44","url":null,"abstract":"The present work demonstrates that the pencil glide mechanism is a physically reliable and a computationally efficient model to simulate the nonlinear behaviour of b.c.c. single and polycrystals. For that purpose, the pencil glide extension of Schmid’s criterion used by Gilormini [1] is incorporated in a single crystal model and in a homogenized polycrystal model accounting for large elastoviscoplastic deformations. The response of the pencil glide model in terms of stress-strain curves and lattice rotation is compared to the prediction based on the consideration of all ({110}〈111〉+ {112}〈111〉) slip systems. In the case of α-iron single crystals both approaches are shown to accurately reproduce recent experimental results [2, 3]. The comparison is extended to α-iron polycrystals behaviour under tension, compression, rolling and simple shear loading conditions. The evolution of crystallographic textures obtained either based on pencil glide or using the 24 slip systems is analyzed and compared to classical experimental results from the literature. Limitations of the approach, especially in the case of simple shear textures, are also pointed out. The pencil glide approach can be viewed as a reduced order model enhancing computational efficiency of crystal plasticity simulations involving many slip mechanisms.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84129049","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 present manuscript is devoted to two works related to the spontaneous formation of patterns in Nature: venation in leaves and evolution of embryos. Morphogenetic processes and growth-induced instability phenomena are modelled through analogue experiments. The organization of veins in leaves is similar to what is expected from growth in a tensorial stress field that governs the formation of fractures, while the change in the shape of embryos is related to the deformation of a shell-like membrane whose properties evolve with time. The approaches resulting from analogue experiments is a way to explore specific properties of the media at a macroscopic scale. Thus the manuscript aims to focus on the analogue experiments, their adaptability to reproduce specific patterns and the relation between both growth-induced instability and mechanical behaviour of the matter.
{"title":"Morphogenetic processes: from leaves to embryos","authors":"L. Pauchard","doi":"10.5802/crmeca.33","DOIUrl":"https://doi.org/10.5802/crmeca.33","url":null,"abstract":"The present manuscript is devoted to two works related to the spontaneous formation of patterns in Nature: venation in leaves and evolution of embryos. Morphogenetic processes and growth-induced instability phenomena are modelled through analogue experiments. The organization of veins in leaves is similar to what is expected from growth in a tensorial stress field that governs the formation of fractures, while the change in the shape of embryos is related to the deformation of a shell-like membrane whose properties evolve with time. The approaches resulting from analogue experiments is a way to explore specific properties of the media at a macroscopic scale. Thus the manuscript aims to focus on the analogue experiments, their adaptability to reproduce specific patterns and the relation between both growth-induced instability and mechanical behaviour of the matter.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74459822","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 report a phenomenon of phase separation that relates in many aspects to Yves Couder's work: an inflatable architectured elastomer plate, expected to expand homogeneously in its plane, buckles instead widely out-of-plane into very complex shape when internal pressure is applied. We show that this morphogenetic pattern formation is due to a two-dimensional elastic phase separation, which induces incompatible patchy non-Euclidean reference metric.
{"title":"Morphogenesis through elastic phase separation in a pneumatic surface","authors":"Emmanuel Si'efert, B. Roman","doi":"10.5802/crmeca.43","DOIUrl":"https://doi.org/10.5802/crmeca.43","url":null,"abstract":"We report a phenomenon of phase separation that relates in many aspects to Yves Couder's work: an inflatable architectured elastomer plate, expected to expand homogeneously in its plane, buckles instead widely out-of-plane into very complex shape when internal pressure is applied. We show that this morphogenetic pattern formation is due to a two-dimensional elastic phase separation, which induces incompatible patchy non-Euclidean reference metric.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87534650","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 2008, we published an article proposing that the microtubular cytoskeleton in plants use maximal tensile stress directions to guide organ growth [1]. Yves Couder was instrumental in that project. Here are some memories and prospects from this collaborative and interdisciplinary endeavor.
{"title":"Yves Couder: Putting mechanics back into the shoot apical meristem","authors":"J. Traas, O. Hamant","doi":"10.5802/crmeca.19","DOIUrl":"https://doi.org/10.5802/crmeca.19","url":null,"abstract":"In 2008, we published an article proposing that the microtubular cytoskeleton in plants use maximal tensile stress directions to guide organ growth [1]. Yves Couder was instrumental in that project. Here are some memories and prospects from this collaborative and interdisciplinary endeavor.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84655478","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 rapid cell growth that is associated with the formation of new lateral organs in the shoot apical meristem was linked to an increase in cell wall elasticity but not viscosity in the plant model Arabidopsis thaliana. To investigate the generality of this puzzling relationship, we explored in seven plant species, covering a wide diversity across land plants, the changes in mechanical properties of the cell walls that occur during organ formation. We show that, despite the considerable variation in cell wall composition among the species tested, a drop in cell wall stiffness systematically accompanied primordia formation. We also observed that meristem activity correlates with cell wall elasticity in three species. Thus it seems that cell wall elasticity and growth rate in the meristem are correlated across the land plants.
{"title":"Exploring the relation between apical growth, organ formation and cell wall mechanics across land plant species","authors":"A. Peaucelle","doi":"10.5802/crmeca.28","DOIUrl":"https://doi.org/10.5802/crmeca.28","url":null,"abstract":"The rapid cell growth that is associated with the formation of new lateral organs in the shoot apical meristem was linked to an increase in cell wall elasticity but not viscosity in the plant model Arabidopsis thaliana. To investigate the generality of this puzzling relationship, we explored in seven plant species, covering a wide diversity across land plants, the changes in mechanical properties of the cell walls that occur during organ formation. We show that, despite the considerable variation in cell wall composition among the species tested, a drop in cell wall stiffness systematically accompanied primordia formation. We also observed that meristem activity correlates with cell wall elasticity in three species. Thus it seems that cell wall elasticity and growth rate in the meristem are correlated across the land plants.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79574170","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}
When liquid nitrogen is set into rotation in a warm pot, the surface, initially forming an axissymmetrical, toroidal shape, spontaneously re-structures into a series of rotating polygons with a diminishing number of corners, while slowing down. This spontaneous “ordering” occurs despite the violently turbulent and boiling state of the fluid. We show experimentally that these shapes are well-described as a sum of a few Fourier modes, and we present experimental results for the development of the frequencies and amplitudes of these wave-modes during the transient process. We compare our results with the theoretical results for the instabilities of a potential vortex flow and argue that the first polygon formed in the transient process should be described by this theory. The paper is dedicated to the memory of Yves Couder, colleague, friend and a life-long source of inspiration. Résumé. Dans cet article nous nous intéressons au cas d’un volume d’azote liquide en état de caléfaction mis en rotation dans un récipient cylindrique chauffé. La surface libre du liquide, initialement sous forme d’un tore axisymétrique, va se déstabiliser et se restructurer en une série de polygones tournants dont le nombre de côtés diminue à mesure que le liquide ralentit. Ce facettage apparaît spontanément alors même que le liquide connait une violente ébullition et un écoulement extrêmement turbulent. Nous démontrons expérimentalement que les formes observées peuvent être décrites par la combinaison d’un petit nombre de modes de Fourier et nous étudions l’évolution de ces modes en termes d’amplitude et de fréquence depuis le premier polygone visible jusqu’à la fin de la rotation du liquide. Nous comparons nos résultats expérimentaux avec un modèle théorique décrivant la perte de stabilité des écoulements de type vortex potentiel et nous soutenons que le premier polygone observable suite à la déstabilisation de la forme axisymétrique peut être décrit par ce modèle. Cet article est dédié à la mémoire d’Yves Couder qui fut pour nous un collègue, un ami et une intarissable source d’inspiration.
当液氮在一个温暖的锅中旋转时，表面最初形成一个轴对称的环形，自发地重新结构成一系列旋转的多边形，角的数量越来越少，同时减速。尽管流体处于剧烈的湍流和沸腾状态，这种自发的“排序”还是会发生。我们通过实验证明，这些形状可以很好地描述为几个傅立叶模态的总和，并且我们提出了这些波模态在瞬态过程中频率和振幅发展的实验结果。我们将结果与势涡不稳定性的理论结果进行了比较，并认为在瞬态过程中形成的第一个多边形应该用该理论来描述。这篇论文是为了纪念伊夫·库德，他是我的同事、朋友和一生的灵感来源。的简历。第2条规定:在液体液体体积和液体体积之间的交换，在液体液体体积和液体液体体积之间的交换，在液体液体体积和液体液体体积之间的交换。La surface libre du liquide，初始化sous form d 'un tore axisymsamtrique, va se dsamri稳定器和se restructorator in une ssamriride polygones流动者不允许使用nombre de côtés减少conmesure que le liquident。自动调制器自动调制器même有液体调制器，有暴力调制器，有震荡调制器，有震荡调制器extrêmement。目前的情况是，在实验过程中，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况下，已观察到的情况。有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较，没有比较的比较。这篇文章测试了伊夫·库德(yves Couder)的职业生涯中，他的职业生涯中有很多的同事，他们是一个无形的灵感来源。
{"title":"Shape dynamics of rotating polygons on the surface of liquid nitrogen in a Leidenfrost state","authors":"Jacob Bach, A. Duchesne, T. Bohr","doi":"10.5802/crmeca.24","DOIUrl":"https://doi.org/10.5802/crmeca.24","url":null,"abstract":"When liquid nitrogen is set into rotation in a warm pot, the surface, initially forming an axissymmetrical, toroidal shape, spontaneously re-structures into a series of rotating polygons with a diminishing number of corners, while slowing down. This spontaneous “ordering” occurs despite the violently turbulent and boiling state of the fluid. We show experimentally that these shapes are well-described as a sum of a few Fourier modes, and we present experimental results for the development of the frequencies and amplitudes of these wave-modes during the transient process. We compare our results with the theoretical results for the instabilities of a potential vortex flow and argue that the first polygon formed in the transient process should be described by this theory. The paper is dedicated to the memory of Yves Couder, colleague, friend and a life-long source of inspiration. Résumé. Dans cet article nous nous intéressons au cas d’un volume d’azote liquide en état de caléfaction mis en rotation dans un récipient cylindrique chauffé. La surface libre du liquide, initialement sous forme d’un tore axisymétrique, va se déstabiliser et se restructurer en une série de polygones tournants dont le nombre de côtés diminue à mesure que le liquide ralentit. Ce facettage apparaît spontanément alors même que le liquide connait une violente ébullition et un écoulement extrêmement turbulent. Nous démontrons expérimentalement que les formes observées peuvent être décrites par la combinaison d’un petit nombre de modes de Fourier et nous étudions l’évolution de ces modes en termes d’amplitude et de fréquence depuis le premier polygone visible jusqu’à la fin de la rotation du liquide. Nous comparons nos résultats expérimentaux avec un modèle théorique décrivant la perte de stabilité des écoulements de type vortex potentiel et nous soutenons que le premier polygone observable suite à la déstabilisation de la forme axisymétrique peut être décrit par ce modèle. Cet article est dédié à la mémoire d’Yves Couder qui fut pour nous un collègue, un ami et une intarissable source d’inspiration.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87480046","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. 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":null,"pages":null},"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}
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