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Pomeau Y, Le Berre M. Quantum mechanics: how to use Everett theory practically. EPJ Web Conf 2022. [DOI: 10.1051/epjconf/202226301010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Among theories of the physical world, quantum mechanics remains a topic of lively discussions on its so-called interpretation. For some it remains an open question to understand how deterministic equations of this theory, as established long ago, may combine with a fundamental uncertainty. We consider the process of spontaneous emission by an atom interacting with infinite number of degrees of freedom of the electromagnetic field. There is uncertainty in the evolution of the photo-emission process which was characterized as Markovian by using the equations of quantum mechanics when the decay of the atom is due to the coupling with the vacuum field. The Markovian property leads us naturally to describe spontaneous emission by using the classical Kolmogorov equation for the probability evolution of a parameter defining the state of the atom. We explain that Everett’s many-worlds interpretation weld together our description, and appears therefore as a consequence of the equations of quantum mechanics, that solves in this case the riddle of deterministic equations describing random events.
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Abstract
Dicing soft solids with a sharp knife is quicker and smoother if the blade is sliding rapidly parallel to its edge in addition to the normal squeezing motion. We explain this common observation with a consistent theory suited for soft gels and departing from the standard theories of elastic fracture mechanics relied on for a century. The gel is assumed to fail locally when submitted to stresses exceeding a threshold σ_{1}. The changes in its structure generate a liquid layer coating the blade and transmitting the stress through viscous forces. The driving parameters are the ratio U/W of the normal to the tangential velocity of the blade, and the characteristic length ηW/σ_{1}, with η the viscosity of the liquid layer. The existence of a maximal value of U/W for a steady regime explains the crucial role of the tangential velocity for slicing biological and other soft materials.
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Affiliation(s)
- Serge Mora
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier and CNRS, 34090 Montpellier, France
| | - Yves Pomeau
- LadHyX, UMR CNRS 7646, Ecole Polytechnique, 91128 Palaiseau, France
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Josserand C, Le Berre M, Pomeau Y. Scaling laws in turbulence. Chaos 2020; 30:073137. [PMID: 32752609 DOI: 10.1063/1.5144147] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
Following the idea that dissipation in turbulence at high Reynolds number is dominated by singular events in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows, scaling laws should depend only on quantities appearing in the Euler equations. This excludes viscosity or a turbulent length as scaling parameters and constrains drastically possible analytical pictures of this limit. We focus on the drag law deduced by Newton for a projectile moving quickly in a fluid at rest. Inspired by this Newton's drag force law (proportional to the square of the speed of the moving object in the limit of large Reynolds numbers), which is well verified in experiments when the location of the detachment of the boundary layer is defined, we propose an explicit relationship between the Reynolds stress in the turbulent wake and quantities depending on the velocity field (averaged in time but depending on space). This model takes the form of an integrodifferential equation for the velocity which is eventually solved for a Poiseuille flow in a circular pipe.
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Affiliation(s)
| | - Martine Le Berre
- Ladhyx (CNRS UMR 7646), Ecole Polytechnique, 91128 Palaiseau, France
| | - Yves Pomeau
- Ladhyx (CNRS UMR 7646), Ecole Polytechnique, 91128 Palaiseau, France
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Tran MB, Pomeau Y. Boltzmann-type collision operators for Bogoliubov excitations of Bose-Einstein condensates: A unified framework. Phys Rev E 2020; 101:032119. [PMID: 32289980 DOI: 10.1103/physreve.101.032119] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2019] [Accepted: 02/20/2020] [Indexed: 11/07/2022]
Abstract
Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Einstein condensate, we derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the commutators, we find three collisional processes. One of them describes the 1↔2 interactions between the condensate and the excited atoms. The other two describe the 2↔2 and 1↔3 interactions between the excited atoms themselves.
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Affiliation(s)
- Minh-Binh Tran
- Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA
| | - Yves Pomeau
- LadHyX-Laboratoire d'hydrodynamique, Ladhyx, Ecole Polytechnique, Palaiseau, France
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Abstract
We revisit the problem on the inner structure of shock waves in simple gases modelized by the Boltzmann kinetic equation. In a paper by Pomeau [Y. Pomeau, Transp. Theory Stat. Phys. 16, 727 (1987)10.1080/00411458708204311], a self-similarity approach was proposed for infinite total cross section resulting from a power-law interaction, but this self-similar form does not have finite energy. Motivated by the work of Pomeau [Y. Pomeau, Transp. Theory Stat. Phys. 16, 727 (1987)10.1080/00411458708204311] and Bobylev and Cercignani [A. V. Bobylev and C. Cercignani, J. Stat. Phys. 106, 1039 (2002)10.1023/A:1014037804043], we started the research on the rigorous study of the solutions of the spatial homogeneous Boltzmann equation, focusing on those which do not have finite energy. However, infinite energy solutions do not have physical meaning in the present framework of kinetic theory of gases with collisions conserving the total kinetic energy. In the present work, we provide a correction to the self-similar form, so that the solutions are more physically sound in the sense that the energy is no longer infinite and that the perturbation brought by the shock does not grow at large distances of it on the cold side in the soft potential case.
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Affiliation(s)
- Yves Pomeau
- LadHyX, Laboratoire d'hydrodynamique, Ladhyx, Ecole Polytechnique, 91120 Palaiseau, France
| | - Minh-Binh Tran
- Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA
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Pomeau Y, Tran MB. Shock waves from the inhomogeneous Boltzmann equation. Phys Rev E 2020; 100:062120. [PMID: 31962387 DOI: 10.1103/physreve.100.062120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2019] [Indexed: 11/07/2022]
Abstract
We revisit the problem on the inner structure of shock waves in simple gases modelized by the Boltzmann kinetic equation. In a paper by Pomeau [Y. Pomeau, Transp. Theory Stat. Phys. 16, 727 (1987)10.1080/00411458708204311], a self-similarity approach was proposed for infinite total cross section resulting from a power-law interaction, but this self-similar form does not have finite energy. Motivated by the work of Pomeau [Y. Pomeau, Transp. Theory Stat. Phys. 16, 727 (1987)10.1080/00411458708204311] and Bobylev and Cercignani [A. V. Bobylev and C. Cercignani, J. Stat. Phys. 106, 1039 (2002)10.1023/A:1014037804043], we started the research on the rigorous study of the solutions of the spatial homogeneous Boltzmann equation, focusing on those which do not have finite energy. However, infinite energy solutions do not have physical meaning in the present framework of kinetic theory of gases with collisions conserving the total kinetic energy. In the present work, we provide a correction to the self-similar form, so that the solutions are more physically sound in the sense that the energy is no longer infinite and that the perturbation brought by the shock does not grow at large distances of it on the cold side in the soft potential case.
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Affiliation(s)
- Yves Pomeau
- LadHyX, Laboratoire d'hydrodynamique, Ladhyx, Ecole Polytechnique, 91120 Palaiseau, France
| | - Minh-Binh Tran
- Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA
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Coullet P, Pomeau Y. Light, water and physics in Monet painting. EPJ Web Conf 2020. [DOI: 10.1051/epjconf/202024401011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A common observation is the one of reflection of the Sun or the Moon by the slightly perturbed surface of water. In ”Impression, soleil levant”, now in Marmottant museum in Paris, Monet painted the luminous stripe resulting of this reflection when the source is low on the horizon. As we explain this stripe originates from the fluctuations of the angle of the reflecting surface when they are big enough to spread the multiple images to make them overlap, which requires that the fluctuations of the surface angle are of the same order as the angle of the Sun (or Moon) above the horizon. At higher angle the stripe become a set of non overlapping points representing each the reflected image of the source. This makes an interesting percolation transition by a continuous change of a parameter.
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Abstract
Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An equilibrium configuration results from the interplay between gravity that tends to deform the cylinders downwards under their own weight, and elasticity that resists these distortions. The corresponding steady state exhibits fascinating shapes which are measured with lab-based micro-tomography. For any given initial radius to height ratio, the deformed cylinders are no longer axially symmetric beyond a critical value of a control parameter that depends on the volume force, the height and the elastic modulus: self-similar wrinkling hierarchies develop, and dimples appear at the bottom surface of the shallowest samples. We show that these patterns are the consequences of elastic instabilities.
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Affiliation(s)
- Serge Mora
- Laboratoire de Mécanique et de Génie Civil, Université de Montpellier and CNRS, 163 rue Auguste Broussonnet, F-34090 Montpellier, France.
| | - Edward Andò
- Laboratoire 3SR, Université Grenoble Alpes and CNRS, F-38041 Grenoble, France
| | - Jean-Marc Fromental
- Laboratoire Charles Coulomb, Université de Montpellier and CNRS, 163 rue Auguste Broussonnet, F-34090 Montpellier, France
| | - Ty Phou
- Laboratoire Charles Coulomb, Université de Montpellier and CNRS, 163 rue Auguste Broussonnet, F-34090 Montpellier, France
| | - Yves Pomeau
- University of Arizona, Department of Mathematics, Tucson, USA
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Guo S, Domanov Y, Donovan M, Ducos B, Pomeau Y, Gourier C, Perez E, Luengo GS. Anisotropic cellular forces support mechanical integrity of the Stratum Corneum barrier. J Mech Behav Biomed Mater 2019; 92:11-23. [PMID: 30654216 DOI: 10.1016/j.jmbbm.2018.12.027] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2018] [Revised: 11/26/2018] [Accepted: 12/20/2018] [Indexed: 11/30/2022]
Abstract
The protective function of biological surfaces that are exposed to the exterior of living organisms is the result of a complex arrangement and interaction of cellular components. This is the case for the most external cornified layer of skin, the stratum corneum (SC). This layer is made of corneocytes, the elementary 'flat bricks' that are held together through adhesive junctions. Despite the well-known protective role of the SC under high mechanical stresses and rapid cell turnover, the subtleties regarding the adhesion and mechanical interaction among the individual corneocytes are still poorly known. Here, we explore the adhesion of single corneocytes at different depths of the SC, by pulling them using glass microcantilevers, and measuring their detachment forces. We measured their interplanar adhesion between SC layers, and their peripheral adhesion among cells within a SC layer. Both adhesions increased considerably with depth. At the SC surface, with respect to adhesion, the corneocyte population exhibited a strong heterogeneity, where detachment forces differed by more than one order of magnitude for corneocytes located side by side. The measured detachment forces indicated that in the upper-middle layers of SC, the peripheral adhesion was stronger than the interplanar one. We conclude that the stronger peripheral adhesion of corneocytes in the SC favors an efficient barrier which would be able to resist strong stresses.
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Affiliation(s)
- Shuo Guo
- Laboratoire de Physique Statistique, Ecole Normale Supérieure, l'université de recherche Paris Sciences et Lettres, CNRS UMR 8550, Sorbonne Universités, Université Pierre-et-Marie-Curie (UPMC) University of Paris 06, Université Paris Diderot, 75005 Paris, France
| | - Yegor Domanov
- L'Oréal Research and Innovation, Aulnay-sous-Bois, France
| | - Mark Donovan
- L'Oréal Research and Innovation, Aulnay-sous-Bois, France
| | - Bertrand Ducos
- Laboratoire de Physique Statistique, Ecole Normale Supérieure, l'université de recherche Paris Sciences et Lettres, CNRS UMR 8550, Sorbonne Universités, Université Pierre-et-Marie-Curie (UPMC) University of Paris 06, Université Paris Diderot, 75005 Paris, France
| | - Yves Pomeau
- University of Arizona, Department of Mathematics, Tucson, AZ, USA
| | - Christine Gourier
- Laboratoire de Physique Statistique, Ecole Normale Supérieure, l'université de recherche Paris Sciences et Lettres, CNRS UMR 8550, Sorbonne Universités, Université Pierre-et-Marie-Curie (UPMC) University of Paris 06, Université Paris Diderot, 75005 Paris, France
| | - Eric Perez
- Laboratoire de Physique Statistique, Ecole Normale Supérieure, l'université de recherche Paris Sciences et Lettres, CNRS UMR 8550, Sorbonne Universités, Université Pierre-et-Marie-Curie (UPMC) University of Paris 06, Université Paris Diderot, 75005 Paris, France.
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Richard F, Chakrabarti A, Audoly B, Pomeau Y, Mora S. Buckling of a spinning elastic cylinder: linear, weakly nonlinear and post-buckling analyses. Proc Math Phys Eng Sci 2018. [DOI: 10.1098/rspa.2018.0242] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
An elastic cylinder spinning about a rigid axis buckles beyond a critical angular velocity, by an instability driven by the centrifugal force. This instability and the competition between the different buckling modes are investigated using analytical calculations in the linear and weakly nonlinear regimes, complemented by numerical simulations in the fully post-buckled regime. The weakly nonlinear analysis is carried out for a generic incompressible hyperelastic material. The key role played by the quadratic term in the expansion of the strain energy density is pointed out: this term has a strong effect on both the nature of the bifurcation, which can switch from supercritical to subcritical, and the buckling amplitude. Given an arbitrary hyperelastic material, an equivalent shear modulus is proposed, allowing the main features of the instability to be captured by an equivalent neo-Hookean model.
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Affiliation(s)
- Franck Richard
- Laboratoire de Mécanique et de Génie Civil, Université de Montpellier and CNRS, 163 rue Auguste Broussonnet, Montpellier 34090, France
| | - Aditi Chakrabarti
- Laboratoire de Mécanique et de Génie Civil, Université de Montpellier and CNRS, 163 rue Auguste Broussonnet, Montpellier 34090, France
- Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA 18015, USA
| | - Basile Audoly
- Laboratoire de Mécanique des Solides, École Polytechnique and CNRS, 91128 Palaiseau, France
- Division of Applied Science and Engineering, California Institute of Technology, Pasadena, CA 91125, USA
| | - Yves Pomeau
- Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
| | - Serge Mora
- Laboratoire de Mécanique et de Génie Civil, Université de Montpellier and CNRS, 163 rue Auguste Broussonnet, Montpellier 34090, France
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Chakrabarti A, Chaudhury MK, Mora S, Pomeau Y. Elastobuoyant Heavy Spheres: A Unique Way to Study Nonlinear Elasticity. Phys Rev X 2016; 6:041066. [DOI: 10.1103/physrevx.6.041066] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/19/2023]
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Abstract
This research introduces a new drop fluidics that uses a deformable and stretchable elastomeric film as the platform instead of the commonly used rigid supports. Such a soft film impregnated with magnetic particles can be modulated with an external electromagnetic field that produces a vast array of topographical landscapes with varying surface curvature, which, in conjunction with capillarity, can direct and control the motion of water droplets efficiently and accurately. When a thin layer of oil is present on this film that is deformed locally, a centrosymmetric wedge is formed. A water droplet placed on this oil-laden film becomes asymmetrically deformed, thus producing a gradient of Laplace pressure within the droplet and setting it in motion. A simple theory is presented that accounts for the droplet speed in terms of such geometric variables as the volume of the droplet and the thickness of the oil film covering the soft elastomeric film as well as material variables such as the viscosity of the oil and the interfacial tension of the oil-water interfaces. Following the verification of the theoretical result using well-controlled model systems, we demonstrate how the electromagnetically controlled elastocapillary force can be used to manipulate the motion of single and/or multiple droplets on the surface of the elastomeric film and how elementary operations such as drop fusion and thermally addressed chemical transformation can be carried out in aqueous droplets. It is expected that the resulting drop fluidics would be suitable for the digital control of drop motion by simply switching on and off the electromagnetic fields applied at different positions underneath the elastomeric film in a Boolean sequence. We anticipate that this method of directing and manipulating water droplets is poised for application in various biochemical reaction engineering situations, an example of which is the polymerase chain reaction (PCR).
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Affiliation(s)
- Saheli Biswas
- Department of Chemical and Biomolecular Engineering, Lehigh University , Bethlehem, Pennsylvania 18015, United States
| | - Yves Pomeau
- University of Arizona , Department of Mathematics, Tucson, Arizona 85721, United States
| | - Manoj K Chaudhury
- Department of Chemical and Biomolecular Engineering, Lehigh University , Bethlehem, Pennsylvania 18015, United States
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Pomeau Y, Louët S. Interview with Yves Pomeau, Boltzmann Medallist 2016 : The universality of statistical physics interpretation is ever more obvious. Eur Phys J E Soft Matter 2016; 39:67. [PMID: 27349556 DOI: 10.1140/epje/i2016-16067-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2016] [Accepted: 06/01/2016] [Indexed: 06/06/2023]
Abstract
During the StatPhys Conference on 20th July 2016 in Lyon, France, Yves Pomeau and Daan Frenkel will be awarded the most important prize in the field of Statistical Mechanics: the 2016 Boltzmann Medal, named after the Austrian physicist and philosopher Ludwig Boltzmann. The award recognises Pomeau's key contributions to the Statistical Physics of non-equilibrium phenomena in general. And, in particular, for developing our modern understanding of fluid mechanics, instabilities, pattern formation and chaos. He is recognised as an outstanding theorist bridging disciplines from applied mathematics to statistical physics with a profound impact on the neighbouring fields of turbulence and mechanics. In the article Sabine Louët interviews Pomeau, who is an Editor for the European Physical Journal Special Topics. He shares his views and tells how he experienced the rise of Statistical Mechanics in the past few decades. He also touches upon the need to provide funding to people who have the rare ability to discover new things and ideas, and not just those who are good at filling in grant application forms.
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Affiliation(s)
| | - Sabine Louët
- SciencePOD.net, 6/9 Trinity Street, Dublin 2, Ireland
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Mora S, Pomeau Y. Softening of edges of solids by surface tension. J Phys Condens Matter 2015; 27:194112. [PMID: 25923202 DOI: 10.1088/0953-8984/27/19/194112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Surface tension tends to minimize the area of interfaces between pieces of matter in different thermodynamic phases, be they in the solid or the liquid state. This can be relevant for the macroscopic shape of very soft solids and lead to a roughening of initially sharp edges. We calculate this effect for a Neo-Hookean elastic solid, with assumptions corresponding to actual experiments, namely the case where an initially sharp edge is rounded by the effect of surface tension felt when the fluid surrounding the soft solid (and so surface tension) is changed at the solid/liquid boundary. We consider two opposite limits where the analysis can be carried to the end, the one of a shallow angle and the one of a very sharp angle. Both cases yield a discontinuity of curvature in the state with surface tension although the initial state had a discontinuous slope.
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Affiliation(s)
- Serge Mora
- Laboratoire de Mécanique et de Génie Civil, UMR 5508, Université Montpellier 2-CNRS, Place Eugène Bataillon, F-34095 Montpellier Cedex, France
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Abstract
We demonstrate the instability of the free surface of a soft elastic solid facing downwards. Experiments are carried out using a gel of constant density ρ, shear modulus μ, put in a rigid cylindrical dish of depth h. When turned upside down, the free surface of the gel undergoes a normal outgoing acceleration g. It remains perfectly flat for ρgh/μ<α* with α*≃6, whereas a steady pattern spontaneously appears in the opposite case. This phenomenon results from the interplay between the gravitational energy and the elastic energy of deformation, which reduces the Rayleigh waves celerity and vanishes it at the threshold.
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Affiliation(s)
- Serge Mora
- Laboratoire de Mécanique et de Génie Civil, UMR 5508, Université Montpellier 2 and CNRS, Place Eugène Bataillon, F-34095 Montpellier Cedex, France
| | - Ty Phou
- Laboratoire Charles Coulomb, UMR 5521, Université Montpellier 2 and CNRS, Place Eugène Bataillon, F-34095 Montpellier Cedex, France
| | - Jean-Marc Fromental
- Laboratoire Charles Coulomb, UMR 5521, Université Montpellier 2 and CNRS, Place Eugène Bataillon, F-34095 Montpellier Cedex, France
| | - Yves Pomeau
- Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA
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Pomeau Y, Le Berre M, Chavanis PH, Denet B. Supernovae: an example of complexity in the physics of compressible fluids. Eur Phys J E Soft Matter 2014; 37:26. [PMID: 24771236 DOI: 10.1140/epje/i2014-14026-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2013] [Accepted: 10/25/2013] [Indexed: 06/03/2023]
Abstract
Because the collapse of massive stars occurs in a few seconds, while the stars evolve on billions of years, the supernovae are typical complex phenomena in fluid mechanics with multiple time scales. We describe them in the light of catastrophe theory, assuming that successive equilibria between pressure and gravity present a saddle-center bifurcation. In the early stage we show that the loss of equilibrium may be described by a generic equation of the Painlevé I form. This is confirmed by two approaches, first by the full numerical solutions of the Euler-Poisson equations for a particular pressure-density relation, secondly by a derivation of the normal form of the solutions close to the saddle-center. In the final stage of the collapse, just before the divergence of the central density, we show that the existence of a self-similar collapsing solution compatible with the numerical observations imposes that the gravity forces are stronger than the pressure ones. This situation differs drastically in its principle from the one generally admitted where pressure and gravity forces are assumed to be of the same order. Moreover it leads to different scaling laws for the density and the velocity of the collapsing material. The new self-similar solution (based on the hypothesis of dominant gravity forces) which matches the smooth solution of the outer core solution, agrees globally well with our numerical results, except a delay in the very central part of the star, as discussed. Whereas some differences with the earlier self-similar solutions are minor, others are very important. For example, we find that the velocity field becomes singular at the collapse time, diverging at the center, and decreasing slowly outside the core, whereas previous works described a finite velocity field in the core which tends to a supersonic constant value at large distances. This discrepancy should be important for explaining the emission of remnants in the post-collapse regime. Finally we describe the post-collapse dynamics, when mass begins to accumulate in the center, also within the hypothesis that gravity forces are dominant.
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Affiliation(s)
- Yves Pomeau
- Department of Mathematics, University of Arizona, 85721, Tucson, AZ, USA
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Abstract
We experimentally investigate the Leidenfrost effect at pressures ranging from 1 to 0.05 atmospheric pressure. As a direct consequence of the Clausius–Clapeyron phase diagram of water, the droplet temperature can be at ambient temperature in a non-sophisticated lab environment. Furthermore, the lifetime of the Leidenfrost droplet is significantly increased in this low pressure environment. The temperature and pressure dependence of the evaporation rate is successfully tested against a recently proposed model. These results may pave the way for reaching efficient Leidenfrost micro-fluidic and milli-fluidic applications.
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Affiliation(s)
- Franck Celestini
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 7366, Université de Nice Sophia-Antipolis, Parc Valrose 06108, Nice Cedex 2, France
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Mora S, Maurini C, Phou T, Fromental JM, Audoly B, Pomeau Y. Solid drops: large capillary deformations of immersed elastic rods. Phys Rev Lett 2013; 111:114301. [PMID: 24074091 DOI: 10.1103/physrevlett.111.114301] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2013] [Indexed: 06/02/2023]
Abstract
Under the effect of surface tension, a blob of liquid adopts a spherical shape when immersed in another fluid. We demonstrate experimentally that soft, centimeter-size elastic solids can exhibit a similar behavior: when immersed into a liquid, a gel having a low elastic modulus undergoes large, reversible deformations. We analyze three fundamental types of deformations of a slender elastic solid driven by surface stress, depending on the shape of its cross section: a circular elastic cylinder shortens in the longitudinal direction and stretches transversally; the sharp edges of a square based prism get rounded off as its cross sections tend to become circular; and a slender, triangular based prism bends. These experimental results are compared to analysis and nonlinear simulations of neo-Hookean solids deformed by surface tension and are found to be in good agreement with each other.
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Affiliation(s)
- Serge Mora
- Laboratoire Charles Coulomb, UMR 5221, Université Montpellier 2 and CNRS, Place Eugène Bataillon, F-34095 Montpellier Cedex, France
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Peters RD, Le Berre M, Pomeau Y. Prediction of catastrophes: an experimental model. Phys Rev E Stat Nonlin Soft Matter Phys 2012; 86:026207. [PMID: 23005845 DOI: 10.1103/physreve.86.026207] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2012] [Revised: 06/22/2012] [Indexed: 06/01/2023]
Abstract
Catastrophes of all kinds can be roughly defined as short-duration, large-amplitude events following and followed by long periods of "ripening." Major earthquakes surely belong to the class of "catastrophic" events. Because of the space-time scales involved, an experimental approach is often difficult, not to say impossible, however desirable it could be. Described in this article is a "laboratory" setup that yields data of a type that is amenable to theoretical methods of prediction. Observations are made of a critical slowing down in the noisy signal of a solder wire creeping under constant stress. This effect is shown to be a fair signal of the forthcoming catastrophe in two separate dynamical models. The first is an "abstract" model in which a time-dependent quantity drifts slowly but makes quick jumps from time to time. The second is a realistic physical model for the collective motion of dislocations (the Ananthakrishna set of equations for unstable creep). Hope thus exists that similar changes in the response to noise could forewarn catastrophes in other situations, where such precursor effects should manifest early enough.
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Mora S, Phou T, Fromental JM, Audoly B, Pomeau Y. Shape of an elastic loop strongly bent by surface tension: experiments and comparison with theory. Phys Rev E Stat Nonlin Soft Matter Phys 2012; 86:026119. [PMID: 23005837 DOI: 10.1103/physreve.86.026119] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2012] [Indexed: 06/01/2023]
Abstract
When a very flexible wire is dipped into a soapy solution, it collapses onto itself. We consider the regions of high curvature where the wire folds back onto itself, enclosing a capillary film. The shapes of these end loops are measured in experiments using soap films and compared to a known similarity solution. The sizes of these structures provide a simple and reliable way to measure surface tension.
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Affiliation(s)
- Serge Mora
- Laboratoire Charles Coulomb, UMR 5221, Université Montpellier 2 and CNRS, Montpellier, France.
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Abstract
We put in evidence the unexpected behavior of Leidenfrost droplets at the later stage of their evaporation. We predict and observe that, below a critical size Rl, the droplets spontaneously take off due to the breakdown of the lubrication regime. We establish the theoretical relation between the droplet radius and its elevation. We predict that the vapor layer thickness increases when the droplets become smaller. A satisfactory agreement is found between the model and the experimental results performed on droplets of water and of ethanol.
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Affiliation(s)
- Franck Celestini
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 7366, Université de Nice Sophia-Antipolis, Parc Valrose 06108 Nice Cedex 2, France
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Abstract
We report the observation of a Plateau instability in a thin filament of solid gel with a very small elastic modulus. A longitudinal undulation of the surface of the cylinder reduces its area thereby triggering capillary instability, but is counterbalanced by elastic forces following the deformation. This competition leads to a nontrivial instability threshold for a solid cylinder. The ratio of surface tension to elastic modulus defines a characteristic length scale. The onset of linear instability is when the radius of the cylinder is one-sixth of this length scale, in agreement with theory presented here.
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Affiliation(s)
- Serge Mora
- Laboratoire des Colloïdes, Verres et Nanomatériaux, UMR 5587, Université Montpellier 2 and CNRS, Place Eugène Bataillon, F-34095 Montpellier Cedex, France.
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Affiliation(s)
- Y Pomeau
- a Laboratoire de Physique Statistique de Ecole Normale Supérieure, Unité de Recherche associée au CNRS 1306 , Associé aux Universités Paris VI et VII , 24 rue Lhomond, Paris Cedex 05 , 75231 , France
- b Department of Mathematics , University of Arizona , Tucson , Arizona , 85721 , USA
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Abstract
In a wide range of conditions, ocean waves break. This can be seen as the manifestation of a singularity in the dynamics of the fluid surface, moving under the effect of the fluid motion underneath. We show that, at the onset of breaking, the wave crest expands in the spanwise direction as the square root of time. This is first derived from a theoretical analysis and then compared with experimental findings. The agreement is excellent.
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Affiliation(s)
- Y Pomeau
- Laboratoire de Physique Statistique, École Normale Supérieure24 rue Lhomond, 75231 Paris Cedex 05, France
| | - T Jamin
- Institut de Recherche sur les Phénomènes Hors Équilibre, UMR 6594, CNRS and Aix-Marseille Université49 rue F. Joliot-Curie, BP146, 13384 Marseille Cedex 13, France
| | - M Le Bars
- Institut de Recherche sur les Phénomènes Hors Équilibre, UMR 6594, CNRS and Aix-Marseille Université49 rue F. Joliot-Curie, BP146, 13384 Marseille Cedex 13, France
| | - P Le Gal
- Institut de Recherche sur les Phénomènes Hors Équilibre, UMR 6594, CNRS and Aix-Marseille Université49 rue F. Joliot-Curie, BP146, 13384 Marseille Cedex 13, France
| | - B Audoly
- Laboratoire de Modélisation en Mécanique, UMR 7607, Université Pierre et Marie Curie4 Place Jussieu, case 162, 75252 Paris Cedex 05, France
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Abstract
The intensity of classical bright solitons propagating in linearly coupled identical fibers can be distributed either in a stable symmetric state at strong coupling or in a stable asymmetric state if the coupling is small enough. In the first case, if the initial state is not the equilibrium state, the intensity may switch periodically from fiber to fiber, while in the second case the asymmetrical state remains forever, with most of its energy in either fiber. The latter situation makes a state of propagation with two exactly reciprocal realizations. In the quantum case, such a situation does not exist as an eigenstate because of the quantum tunneling between the two fibers. Such a tunneling is a purely quantum phenomenon without counterpart in the classical theory. We estimate the rate of tunneling by quantizing a simplified dynamics derived from the original Lagrangian equations with test functions. This tunneling could be within reach of the experiments, particularly if the quantum coherence of the soliton can be maintained over a sufficient amount of time.
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Affiliation(s)
- Yves Pomeau
- Laboratoire de Physique Statistique de l'Ecole normale supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France
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Josserand C, Pomeau Y, Rica S. Coexistence of ordinary elasticity and superfluidity in a model of a defect-free supersolid. Phys Rev Lett 2007; 98:195301. [PMID: 17677624 DOI: 10.1103/physrevlett.98.195301] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2006] [Indexed: 05/16/2023]
Abstract
The mechanical behavior of a supersolid is studied in the framework of a fully explicit model derived from the Gross-Pitaevskii equation without assuming any defect or vacancy. A set of coupled nonlinear partial differential equations plus boundary conditions is derived. The conditions of mechanical equilibrium are studied under external constraints such as steady rotation and external stress. Our model explains the experimentally observed paradoxical behavior: a nonclassical rotational inertia fraction in the limit of small rotation speed but a solidlike elastic response to small stress or an external force field.
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Affiliation(s)
- Christophe Josserand
- Institut Jean Le Rond D'Alembert, CNRS UMR 7190, Case 162, 4 place Jussieu, 75005 Paris, France
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Abstract
We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schrödinger equation as a representative model. We formulate a thermodynamic description of the classical condensation process by using a wave turbulence theory with ultraviolet cutoff. In three dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in two dimensions, in complete analogy with standard Bose-Einstein condensation in quantum systems. On the basis of a modified wave turbulence theory, we show that the nonlinear interaction makes the transition to condensation subcritical. The theory is in quantitative agreement with the numerical integration of the nonlinear Schrödinger equation.
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Roberts DC, Pomeau Y. Casimir-like force arising from quantum fluctuations in a slowly moving dilute Bose-Einstein condensate. Phys Rev Lett 2005; 95:145303. [PMID: 16241666 DOI: 10.1103/physrevlett.95.145303] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2005] [Indexed: 05/05/2023]
Abstract
We calculate a force due to zero-temperature quantum fluctuations on a stationary object in a moving superfluid flow. We model the object by a localized potential varying only in the flow direction and model the flow by a three-dimensional weakly interacting Bose-Einstein condensate at zero temperature. We show that this force exists for any arbitrarily small flow velocity and discuss the implications for the stability of superfluid flow.
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Affiliation(s)
- D C Roberts
- Laboratoire de Physique Statistique de l'Ecole normale supérieure, Paris, France
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Abstract
Cellular structures, as the rolls generated by Rayleigh-Bénard instability, have always been an important topic in nonlinear science. The diffusion of a passive scalar in a given steady cellular flow becomes an interesting question in the limit of a large Péclet number, often realistic. The main result there is that the effective diffusion is somewhere in between the molecular diffusion and the "turbulent" diffusion. A new added twist to this is the reaction-diffusion case, where the front speed is the laminar propagation velocity (without flow) times the Péclet number to the power 1/4. I refine this last result and give the behavior of the prefactor in the Zel'dovich limit of a narrow reaction zone.
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Affiliation(s)
- Yves Pomeau
- Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France.
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Aftalion A, Du Q, Pomeau Y. Dissipative flow and vortex shedding in the Painlevé boundary layer of a Bose-Einstein condensate. Phys Rev Lett 2003; 91:090407. [PMID: 14525168 DOI: 10.1103/physrevlett.91.090407] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2003] [Indexed: 05/24/2023]
Abstract
This paper addresses the drag force and formation of vortices in the boundary layer of a Bose-Einstein condensate stirred by a laser beam following the experiments of Phys. Rev. Lett. 83, 2502 (1999)]. We make our analysis in the frame moving at constant speed where the beam is fixed. We find that there is always a drag around the laser beam. We also analyze the mechanism of vortex nucleation. At low velocity, there are no vortices and the drag has its origin in a wakelike phenomenon: This is a particularity of trapped systems since the density gets small in an extended region. The shedding of vortices starts only at a threshold velocity and is responsible for a large increase in drag. This critical velocity for vortex nucleation is lower than the critical velocity computed for the corresponding 2D problem at the center of the cloud.
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Affiliation(s)
- Amandine Aftalion
- CNRS and Laboratoire Jacques-Louis Lions, Université Paris 6, 175 rue du Chevaleret, 75013 Paris, France
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Le Berre M, Ressayre E, Tallet A, Pomeau Y, Di Menza L. Example of a chaotic crystal: the labyrinth. Phys Rev E Stat Nonlin Soft Matter Phys 2002; 66:026203. [PMID: 12241263 DOI: 10.1103/physreve.66.026203] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2001] [Revised: 04/12/2002] [Indexed: 05/23/2023]
Abstract
Labyrinthine structures often appear as the final steady state of pattern forming systems. Being disordered, they exhibit the same kind of short range positional order as the Newell-Pomeau turbulent crystal. Labyrinths can be seen as a limit case of the texture of disordered rolls with a coherence length of the same order as the wavelength. In the various two-dimensional model equations we looked at, labyrinths and parallel rolls are steady states for the same parameters, their occurrence depending on the initial conditions. Comparing the stability of these two structures, we find that in variational models their energy is very close, rolls always being more stable than labyrinths. For the nonvariational model we propose a numerical experiment which displays a well defined bifurcation from parallel rolls to labyrinths as the more stable state.
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Affiliation(s)
- M Le Berre
- Laboratoire de Photophysique Moléculaire, Bâtiment 210, Université de Paris-Sud, 91405 Orsay Cedex, France
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Thiele U, Velarde MG, Neuffer K, Bestehorn M, Pomeau Y. Sliding drops in the diffuse interface model coupled to hydrodynamics. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 64:061601. [PMID: 11736194 DOI: 10.1103/physreve.64.061601] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2001] [Revised: 08/28/2001] [Indexed: 05/23/2023]
Abstract
Using a film thickness evolution equation derived recently combining long-wave approximation and diffuse interface theory [L. M. Pismen and Y. Pomeau, Phys. Rev. E 62, 2480 (2000)] we study one-dimensional surface profiles for a thin film on an inclined plane. We discuss stationary flat film and periodic solutions including their linear stability. Flat sliding drops are identified as universal profiles, whose main properties do not depend on mean film thickness. The flat drops are analyzed in detail, especially how their velocity, advancing and receding dynamic contact angles and plateau thicknesses depend on the inclination of the plane. A study of nonuniversal drops shows the existence of a dynamical wetting transition with hysteresis between droplike solutions and a flat film with small amplitude nonlinear waves.
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Affiliation(s)
- U Thiele
- Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, 28040 Madrid, Spain
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Thiele U, Velarde MG, Neuffer K, Pomeau Y. Film rupture in the diffuse interface model coupled to hydrodynamics. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 64:031602. [PMID: 11580344 DOI: 10.1103/physreve.64.031602] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2000] [Revised: 04/30/2001] [Indexed: 05/23/2023]
Abstract
The process of dewetting of a thin liquid film is usually described using a long-wave approximation yielding a single evolution equation for the film thickness. This equation incorporates an additional pressure term-the disjoining pressure-accounting for the molecular forces. Recently a disjoining pressure was derived coupling hydrodynamics to the diffuse interface model [L. M. Pismen and Y. Pomeau, Phys. Rev. E 62, 2480 (2000)]. Using the resulting evolution equation as a generic example for the evolution of unstable thin films, we examine the thickness ranges for linear instability and metastability for flat films, the families of stationary periodic and localized solutions, and their linear stability. The results are compared to simulations of the nonlinear time evolution. From this we conclude that, within the linearly unstable thickness range, there exists a well defined subrange where finite perturbations are crucial for the time evolution and the resulting structures. In the remainder of the linearly unstable thickness range the resulting structures are controlled by the fastest flat film mode assumed up to now for the entire linearly unstable thickness range. Finally, the implications for other forms of disjoining pressure in dewetting and for spinodal decomposition are discussed.
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Affiliation(s)
- U Thiele
- Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, 28040 Madrid, Spain
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Pismen LM, Pomeau Y. Disjoining potential and spreading of thin liquid layers in the diffuse-interface model coupled to hydrodynamics. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 62:2480-2492. [PMID: 11088728 DOI: 10.1103/physreve.62.2480] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/1999] [Indexed: 05/23/2023]
Abstract
The hydrodynamic phase field model is applied to the problem of film spreading on a solid surface. The disjoining potential, responsible for modification of the fluid properties near a three-phase contact line, is computed from the solvability conditions of the density field equation with appropriate boundary conditions imposed on the solid support. The equations describing the motion of a spreading film are derived in the lubrication approximation (in the limit of small contact angles). In the case of quasiequilibrium spreading, it is shown that the correct sharp-interface limit is obtained, and sample solutions are obtained by numerical integration. It is further shown that evaporation or condensation may strongly affect the dynamics near the contact line, and that it is necessary to account for kinetic retardation of the interphase transport to build up a consistent theory.
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Affiliation(s)
- LM Pismen
- Department of Chemical Engineering and Minerva Center for Nonlinear Physics of Complex Systems, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Affiliation(s)
- M. Ben Amar
- Laboratoire de Physique Statistique, associé au CNRS, á l'École Normale Supérieure, et aux Universités Paris VI et VII 24 Rue Lhomond, 75231 Paris Cedex 05, France
| | - Y. Pomeau
- Department of Mathematics, Université of Arizona, Tucson, AZ 85721, USA
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Adda-Bedia M, Pomeau Y. Morphological instabilities of dynamic fractures in brittle solids. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1996; 54:5774-5779. [PMID: 9965766 DOI: 10.1103/physreve.54.5774] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Adda-Bedia M, Pomeau Y. Crack instabilities of a heated glass strip. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1995; 52:4105-4113. [PMID: 9963883 DOI: 10.1103/physreve.52.4105] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Hayot F, Pomeau Y. Turbulent domain stabilization in annular flows. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1994; 50:2019-2021. [PMID: 9962204 DOI: 10.1103/physreve.50.2019] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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