Structure Theory

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Serafim Kalliadasis - One of the best experts on this subject based on the ideXlab platform.

  • rigorous coherent Structure Theory for falling liquid films viscous dispersion effects on bound state formation and self organization
    Physics of Fluids, 2011
    Co-Authors: Marc Pradas, Dmitri Tseluiko, Serafim Kalliadasis
    Abstract:

    We examine the interaction of two-dimensional solitary pulses on falling liquid films. We make use of the second-order model derived by Ruyer-Quil and Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000); Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a weighted residual technique. The model includes (second-order) viscous dispersion effects which originate from the streamwise momentum equation and tangential stress balance. These effects play a dispersive role that primarily influences the shape of the capillary ripples in front of the solitary pulses. We show that different physical parameters, such as surface tension and viscosity, play a crucial role in the interaction between solitary pulses giving rise eventually to the formation of bound states consisting of two or more pulses separated by well-defined distances and traveling at the same velocity. By developing a rigorous coherent-Structure Theory, we are able to theoretically predict the pulse-separ...

  • rigorous coherent Structure Theory for falling liquid films viscous dispersion effects on bound state formation and self organization
    arXiv: Fluid Dynamics, 2010
    Co-Authors: Marc Pradas, Dmitri Tseluiko, Serafim Kalliadasis
    Abstract:

    We examine the interaction of two-dimensional solitary pulses on falling liquid films. We make use of the second-order model derived by Ruyer-Quil and Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000); Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a weighted residuals technique. The model includes (second-order) viscous dispersion effects which originate from the streamwise momentum equation and tangential stress balance. These effects play a dispersive role that primarily influences the shape of the capillary ripples in front of the solitary pulses. We show that different physical parameters, such as surface tension and viscosity, play a crucial role in the interaction between solitary pulses giving rise eventually to the formation of bound states consisting of two or more pulses separated by well-defined distances and travelling at the same velocity. By developing a rigorous coherent-Structure Theory, we are able to theoretically predict the pulse-separation distances for which bound states are formed. Viscous dispersion affects the distances at which bound states are observed. We show that the Theory is in very good agreement with computations of the second-order model. We also demonstrate that the presence of bound states allows the film free surface to reach a self-organized state that can be statistically described in terms of a gas of solitary waves separated by a typical mean distance and characterized by a typical density.

Marc Pradas - One of the best experts on this subject based on the ideXlab platform.

  • rigorous coherent Structure Theory for falling liquid films viscous dispersion effects on bound state formation and self organization
    Physics of Fluids, 2011
    Co-Authors: Marc Pradas, Dmitri Tseluiko, Serafim Kalliadasis
    Abstract:

    We examine the interaction of two-dimensional solitary pulses on falling liquid films. We make use of the second-order model derived by Ruyer-Quil and Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000); Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a weighted residual technique. The model includes (second-order) viscous dispersion effects which originate from the streamwise momentum equation and tangential stress balance. These effects play a dispersive role that primarily influences the shape of the capillary ripples in front of the solitary pulses. We show that different physical parameters, such as surface tension and viscosity, play a crucial role in the interaction between solitary pulses giving rise eventually to the formation of bound states consisting of two or more pulses separated by well-defined distances and traveling at the same velocity. By developing a rigorous coherent-Structure Theory, we are able to theoretically predict the pulse-separ...

  • rigorous coherent Structure Theory for falling liquid films viscous dispersion effects on bound state formation and self organization
    arXiv: Fluid Dynamics, 2010
    Co-Authors: Marc Pradas, Dmitri Tseluiko, Serafim Kalliadasis
    Abstract:

    We examine the interaction of two-dimensional solitary pulses on falling liquid films. We make use of the second-order model derived by Ruyer-Quil and Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000); Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a weighted residuals technique. The model includes (second-order) viscous dispersion effects which originate from the streamwise momentum equation and tangential stress balance. These effects play a dispersive role that primarily influences the shape of the capillary ripples in front of the solitary pulses. We show that different physical parameters, such as surface tension and viscosity, play a crucial role in the interaction between solitary pulses giving rise eventually to the formation of bound states consisting of two or more pulses separated by well-defined distances and travelling at the same velocity. By developing a rigorous coherent-Structure Theory, we are able to theoretically predict the pulse-separation distances for which bound states are formed. Viscous dispersion affects the distances at which bound states are observed. We show that the Theory is in very good agreement with computations of the second-order model. We also demonstrate that the presence of bound states allows the film free surface to reach a self-organized state that can be statistically described in terms of a gas of solitary waves separated by a typical mean distance and characterized by a typical density.

Dmitri Tseluiko - One of the best experts on this subject based on the ideXlab platform.

  • rigorous coherent Structure Theory for falling liquid films viscous dispersion effects on bound state formation and self organization
    Physics of Fluids, 2011
    Co-Authors: Marc Pradas, Dmitri Tseluiko, Serafim Kalliadasis
    Abstract:

    We examine the interaction of two-dimensional solitary pulses on falling liquid films. We make use of the second-order model derived by Ruyer-Quil and Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000); Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a weighted residual technique. The model includes (second-order) viscous dispersion effects which originate from the streamwise momentum equation and tangential stress balance. These effects play a dispersive role that primarily influences the shape of the capillary ripples in front of the solitary pulses. We show that different physical parameters, such as surface tension and viscosity, play a crucial role in the interaction between solitary pulses giving rise eventually to the formation of bound states consisting of two or more pulses separated by well-defined distances and traveling at the same velocity. By developing a rigorous coherent-Structure Theory, we are able to theoretically predict the pulse-separ...

  • rigorous coherent Structure Theory for falling liquid films viscous dispersion effects on bound state formation and self organization
    arXiv: Fluid Dynamics, 2010
    Co-Authors: Marc Pradas, Dmitri Tseluiko, Serafim Kalliadasis
    Abstract:

    We examine the interaction of two-dimensional solitary pulses on falling liquid films. We make use of the second-order model derived by Ruyer-Quil and Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000); Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a weighted residuals technique. The model includes (second-order) viscous dispersion effects which originate from the streamwise momentum equation and tangential stress balance. These effects play a dispersive role that primarily influences the shape of the capillary ripples in front of the solitary pulses. We show that different physical parameters, such as surface tension and viscosity, play a crucial role in the interaction between solitary pulses giving rise eventually to the formation of bound states consisting of two or more pulses separated by well-defined distances and travelling at the same velocity. By developing a rigorous coherent-Structure Theory, we are able to theoretically predict the pulse-separation distances for which bound states are formed. Viscous dispersion affects the distances at which bound states are observed. We show that the Theory is in very good agreement with computations of the second-order model. We also demonstrate that the presence of bound states allows the film free surface to reach a self-organized state that can be statistically described in terms of a gas of solitary waves separated by a typical mean distance and characterized by a typical density.

Fumio Hirata - One of the best experts on this subject based on the ideXlab platform.

Peter P Varju - One of the best experts on this subject based on the ideXlab platform.

  • the Structure Theory of nilspaces iii inverse limit representations and topological dynamics
    Advances in Mathematics, 2020
    Co-Authors: Yonatan Gutman, Freddie Manners, Peter P Varju
    Abstract:

    Abstract This paper forms the third part of a series by the authors [12] , [11] concerning the Structure Theory of nilspaces. A nilspace is a compact space X together with closed collections of cubes C n ( X ) ⊆ X 2 n , n = 1 , 2 , … , satisfying some natural axioms. Our goal is to extend the Structure Theory of nilspaces obtained by Antolin Camarena and Szegedy, and to provide new proofs. Our main result is that, under the technical assumption that C n ( X ) is a connected space for all n, then X is isomorphic (in a strong sense) to an inverse limit of nilmanifolds. This is a direct and slight generalization of the main result of Antolin Camarena and Szegedy. We also apply our methods to obtain Structure theorems in the setting of topological dynamics. Specifically, if H is a group (subject to very mild topological assumptions) and ( H , X ) is a minimal dynamical system, then we give a simple characterization of the maximal pronilfactor of X. This generalizes the case H = Z , which is a theorem of Host, Kra and Maass, although even in that case we give a significantly different proof.

  • The Structure Theory of nilspaces I
    'Organisation for Economic Co-Operation and Development (OECD)', 2020
    Co-Authors: Gutman Y, Manners F, Peter P Varju
    Abstract:

    This paper forms the first part of a series by the authors [GMV2,GMV3] concerning the Structure Theory of nilspaces of Antol\'in Camarena and Szegedy. A nilspace is a compact space $X$ together with closed collections of cubes $C^n(X)\subseteq X^{2^n}$, $n=1,2,\ldots$ satisfying some natural axioms. Antol\'in Camarena and Szegedy proved that from these axioms it follows that (certain) nilspaces are isomorphic (in a strong sense) to an inverse limit of nilmanifolds. The aim of our project is to provide a new self-contained treatment of this Theory and give new applications to topological dynamics. This paper provides an introduction to the project from the point of view of applications to higher order Fourier analysis. We define and explain the basic definitions and constructions related to cubespaces and nilspaces and develop the weak Structure Theory, which is the first stage of the proof of the main Structure theorem for nilspaces. Vaguely speaking, this asserts that a nilspace can be built as a finite tower of extensions where each of the successive fibers is a compact abelian group. We also make some modest innovations and extensions to this Theory. In particular, we consider a class of maps that we term fibrations, which are essentially equivalent to what are termed fiber-surjective morphisms by Anatol\'in Camarena and Szegedy, and we formulate and prove a relative analogue of the weak Structure Theory alluded to above for these maps. These results find applications elsewhere in the project.Royal Societ

  • the Structure Theory of nilspaces iii inverse limit representations and topological dynamics
    arXiv: Dynamical Systems, 2016
    Co-Authors: Yonatan Gutman, Freddie Manners, Peter P Varju
    Abstract:

    This paper forms the third part of a series by the authors [GMV1,GMV2] concerning the Structure Theory of nilspaces. A nilspace is a compact space $X$ together with closed collections of cubes $C^n(X)\subseteq X^{2^n}$, $n=1,2,\ldots$, satisfying some natural axioms. Our goal is to extend the Structure Theory of nilspaces obtained by Antol\'in Camarena and Szegedy, and to provide new proofs. Our main result is that, under the technical assumption that $C^n(X)$ is a connected space for all $n$, then $X$ is isomorphic (in a strong sense) to an inverse limit of nilmanifolds. This is a direct and slight generalization of the main result of Antol\'in Camarena and Szegedy. We also apply our methods to obtain Structure theorems in the setting of topological dynamics. Specifically, if $H$ is a group (subject to very mild topological assumptions) and $(H,X)$ is a minimal dynamical system, then we give a simple characterization of the maximal pronilfactor of $X$. This generalizes the case $H = \mathbb{Z}$, which is a theorem of Host, Kra and Maass, although even in that case we give a significantly different proof.