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    Secondary flows in a laterally heated horizontal cylinder  Open access

     Mercader Calvo, Maria Isabel; Sanchez Casals, Odalys de La Caridad; Batiste Boleda, Oriol
    Physics of fluids
    Date of publication: 2014-01-01
    Journal article

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    In this paper we study the problem of thermal convection in a laterally heated, finite, horizontal cylinder. We consider cylinders of moderate aspect ratio (height/diameter approximate to 2) containing a small Prandtl number fluid (sigma < 0.026) typical of molten metals and molten semiconductors. We use the Navier-Stokes and energy equations in the Boussinesq approximation to calculate numerically the basic steady states, analyze their linear stability, and compute some nonlinear secondary flows originated from the instabilities. All the calculated flows and the stability analysis are characterized by their symmetry properties. Due to the confined cylindrical geometry, -presence of lateral walls and lids-, all the flows are completely three dimensional even for the basic steady states. In the range of Prandtl numbers studied, we have identified four different types of instabilities, either oscillatory or stationary. The physical mechanisms, shear or buoyancy, of the corresponding flow transitions have been analyzed. As the value of the Prandtl number approaches sigma = 0.026 the scenario of bifurcations becomes more complicated due to the existence of two different stable basic states originated in a saddle-node bifurcation; a fact that had been overlooked in previous works. (C) 2014 AIP Publishing LLC.

    In this paper we study the problem of thermal convection in a laterally heated, finite, horizontal cylinder. We consider cylinders of moderate aspect ratio (height/diameter approximate to 2) containing a small Prandtl number fluid (sigma < 0.026) typical of molten metals and molten semiconductors. We use the Navier-Stokes and energy equations in the Boussinesq approximation to calculate numerically the basic steady states, analyze their linear stability, and compute some nonlinear secondary flows originated from the instabilities. All the calculated flows and the stability analysis are characterized by their symmetry properties. Due to the confined cylindrical geometry, -presence of lateral walls and lids-, all the flows are completely three dimensional even for the basic steady states. In the range of Prandtl numbers studied, we have identified four different types of instabilities, either oscillatory or stationary. The physical mechanisms, shear or buoyancy, of the corresponding flow transitions have been analyzed. As the value of the Prandtl number approaches sigma = 0.026 the scenario of bifurcations becomes more complicated due to the existence of two different stable basic states originated in a saddle-node bifurcation; a fact that had been overlooked in previous works. (C) 2014 AIP Publishing LLC.

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    Travelling convectons in binary fluid convection  Open access

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Arantxa; Knobloch, Edgar
    Journal of fluid mechanics
    Date of publication: 2013-05
    Journal article

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    Binary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. With no-slip, fixed-temperature, no-mass-flux boundary conditions at the top and bottom stationary odd-and even-parity convectons fall on a pair of intertwined branches connected by branches of travelling asymmetric states. In appropriate parameter regimes the stationary convectons may be stable. When the boundary condition on the top is changed to Newton's law of cooling the odd-parity convectons start to drift and the branch of odd-parity convectons breaks up and reconnects with the branches of asymmetric states. We explore the dependence of these changes and of the resulting drift speed on the associated Biot number using numerical continuation, and compare and contrast the results with a related study of the Swift-Hohenberg equation by Houghton & Knobloch (Phys. Rev. E, vol. 84, 2011, art. 016204).

    Binary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. With no-slip, fixed-temperature, no-mass-flux boundary conditions at the top and bottom stationary odd- and even-parity convectons fall on a pair of intertwined branches connected by branches of travelling asymmetric states. In appropriate parameter regimes the stationary convectons may be stable. When the boundary condition on the top is changed to Newton’s law of cooling the odd-parity convectons start to drift and the branch of odd-parity convectons breaks up and reconnects with the branches of asymmetric states. We explore the dependence of these changes and of the resulting drift speed on the associated Biot number using numerical continuation, and compare and contrast the results with a related study of the Swift–Hohenberg equation by Houghton & Knobloch (Phys. Rev. E, vol. 84, 2011, art. 016204). We use the results to identify stable drifting convectons and employ direct numerical simulations to study collisions between them. The collisions are highly inelastic, and result in convectons whose length exceeds the sum of the lengths of the colliding convectons.

  • Drifting convectons in binary mixtures

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    Bifurcations and Instabilities in Fluid Dynamics
    Presentation's date: 2013-07-08
    Presentation of work at congresses

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  • Stationary and oscillatory secondary flows in a laterally heated horizontal cylinder

     Sanchez Casals, Odalys de La Caridad; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol
    International Couette-Taylor Workshop
    Presentation's date: 2013-06-25
    Presentation of work at congresses

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  • On the accuracy of the Interdiffusion coefficients under real accelerometric ISS conditions

     Sanchez Casals, Odalys de La Caridad; Pujalte, Mónica; Ruiz, Xavier; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Gavaldà, Josefina
    European Low Gravity Research Association Symposium
    Presentation's date: 2013-09-13
    Presentation of work at congresses

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  • Pattern selection near the onset in cylindrical binary mixture convection

     Alonso Maleta, Maria Aranzazu; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol
    Bifurcations and Instabilities in Fluid Dynamics
    Presentation's date: 2013-07-08
    Presentation of work at congresses

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    Thermal convection in a binary fluid layer heated from below is a system that exhibits a great variety of pattern forming phenomena when driven away from equilibrium. In mixtures with a negative Soret coefficient (S < 0), the spatio-temporal properties of the arising flow patterns are known to be complex due to the subcritical oscillatory nature of the primary bifurcation. The two dimensional system has been widely studied, numerically as well as experimentally using annular cells. Near the onset, spatially extended patterns (travelling and standing waves, stationary rolls or spatio-temporal chaotic states) and confined solutions (localized travelling waves and stationary states) have been obtained. The localized stationary states are known to be favoured by the strongly subcritical nature of the steady bifurcation beyond the primary Hopf bifurcation. In the present work, we investigate numerically three dimensional pattern selection in a vertical cylindrical cell heated from below for a water-ethanol mixture. We focus on the spatio temporal dynamics in the neigborhood of the initial oscillatory instability and extend the results presented in [1] by varying the aspect ratio of the container. For highly constrained geometries we obtain that, despite the oscillatory nature of the primary instability, pure thermal stationary modes are selected after long time-dependent transients. For intermediate aspect ratio cylinders, stable oscillatory states seem to coexist with the stationary thermal modes, indicating that concentration begins to play a role in the dynamics. In highly extended cylinders we obtain a diversity of confined patterns, many of which are consistent with experimental observations [2]. Remarkably, though, we have obtained persistent large amplitude highly localized patterns not reported in experiments.

  • Drifting convectons in binary fluid convection

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    International Couette-Taylor Workshop
    Presentation's date: 2013-06-26
    Presentation of work at congresses

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  • Traveling convectons in binary mixtures

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    Dynamics Days Europe
    Presentation's date: 2013-06-05
    Presentation of work at congresses

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  • Binary fluid convection in cylindrical cells

     Alonso Maleta, Maria Aranzazu; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol
    International Couette-Taylor Workshop
    Presentation's date: 2013-06-24
    Presentation of work at congresses

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  • Colliding convectons

     Knobloch, Edgar; Houghton, Steve; Batiste Boleda, Oriol; Mercader Calvo, Maria Isabel; Alonso Maleta, Maria Aranzazu
    Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics
    Presentation's date: 2012-12-04
    Presentation of work at congresses

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  • Secondary Flows in a Laterally Heated Horizontal Cylinder

     Sanchez Casals, Odalys de La Caridad; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol
    International meeting on Thermodiffusion
    Presentation's date: 2012-06-06
    Presentation of work at congresses

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  • Computer generated Earth diffusion processes in liquid binary Al-Cu alloys

     Sanchez Casals, Odalys de La Caridad; Ruiz Marti, Xavier; Batiste Boleda, Oriol; Mercader Calvo, Maria Isabel
    International meeting on Thermodiffusion
    Presentation's date: 2012-06-05
    Presentation of work at congresses

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  • Convectons and drifting convectons in binary mixtures

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    International meeting on Thermodiffusion
    Presentation's date: 2012-06-06
    Presentation of work at congresses

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  • Dissipative solitons in binary fluid convection

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    Discrete and continuous dynamical systems. Series S (paper)
    Date of publication: 2011-10-01
    Journal article

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    A horizontal layer containing a miscible mixture of two fluids can produce dissipative solitons when heated from below. The physics of the system is described, and dissipative solitons are computed using numerical continuation for three distinct sets of experimentally realizable parameter values. The stability of the solutions is investigated using direct numerical integration in time and related to the stability properties of the competing periodic state.

  • Convectons, anticonvectons and multiconvectons in binary fluid convection

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu; Knobloch ., Edgar
    Journal of fluid mechanics
    Date of publication: 2011-01-25
    Journal article

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    Convectons  Open access

     Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol; Knobloch, Edgar; Mercader Calvo, Maria Isabel
    Date of publication: 2011-01-01
    Book chapter

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    A horizontal layer containing a miscible mixture of two fluids can generate dissipative solitons called convectons when heated from below. The physics of the system leading to this behavior is explained, and the properties of the resulting convectons are described. The convectons are shown to be present in a parameter regime known as the pinning region containing a multiplicity of stable convectons of odd and even parity. These lie on solution branches that snake back and forth across the pinning region and illustrate a phenomenon known as homoclinic snaking. Examples of single pulse and multipulse convectons in periodic and closed containers are exhibited and compared with similar states described by the Swift-Hohenberg equation. Time-dependent states in the form of localized traveling waves are computed and distinguished from convectons that drift.

    A horizontal layer containing a miscible mixture of two fluids can generate dissipative solitons called convectons when heated from below. The physics of the system leading to this behavior is explained, and the properties of the resulting convectons are described. The convectons are shown to be present in a parameter regime known as the pinning region containing a multiplicity of stable convectons of odd and even parity. These lie on solution branches that snake back and forth across the pinning region and illustrate a phenomenon known as homoclinic snaking. Examples of single pulse and multipulse convectons in periodic and closed containers are exhibited and compared with similar states described by the Swift-Hohenberg equation. Time-dependent states in the form of localized traveling waves are computed and distinguished from convectons that drift.

    Postprint (author’s final draft)

  • Degenerate bifurcations in binary-mixture convection

     Meca Alvarez, Esteban; Mercader Calvo, Maria Isabel; Ramirez de La Piscina Millan, Laureano
    International Symposium Bifurcations and Instabilities in Fluid Dynamics
    Presentation's date: 2011-07-21
    Presentation of work at congresses

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  • Numerical study of natural convection inside a horizontal cylinder

     Sanchez Casals, Odalys de La Caridad; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol
    Congreso de Física Estadística
    Presentation's date: 2011-06-02
    Presentation of work at congresses

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  • Steady localized states in binary fluid convection

     Mercader Calvo, Maria Isabel
    Simposio Internacional Física de los sistemas fuera de equilibrio
    Presentation's date: 2011-02-18
    Presentation of work at congresses

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  • Convectons, anticonvectons, multiconvectons and drifting convectons in binary mixtures

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    International Symposium Bifurcations and Instabilities in Fluid Dynamics
    Presentation's date: 2011-07-18
    Presentation of work at congresses

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  • Natural convection inside a horizontal cylinder

     Sanchez Casals, Odalys de La Caridad; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol
    International Symposium Bifurcations and Instabilities in Fluid Dynamics
    Presentation's date: 2011-07-18
    Presentation of work at congresses

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  • An efficient spectral code for incompressible flows in cylindrical geometries

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu
    Computers and fluids
    Date of publication: 2010-02
    Journal article

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    An efficient and accurate numerical scheme is proposed to solve the incompressible Navier–Stokes equations in a bounded cylinder. The scheme is based on a projection method formulated in primitive variables to maintain the incompressibility constraint, with a second-order semi-implicit scheme for the time integration, and a pseudospectral approximation for the space variables. The Chebyshev-collocation method applied in the radial and axial directions, and the Fourier–Galerkin approximation used in the azimuthal direction lead to a sequence of two-dimensional Helmholtz and Poisson equations for every azimuthal coefficient that are solved by a diagonalization technique. Radial expansions are considered in the diameter of the cell in order to avoid clustering about the axis, and the number of points are selected to ensure that r=0 is not a collocation point. A minimal number of regularity conditions are imposed implicitly at the origin by forcing the proper parity of the Fourier expansions in the radial direction. The method has been tested on analytical solutions and compared with other reliable three-dimensional results. The improvements introduced in the treatment of the spatial discretization reduce significantly the difficulty of implementation of the code, and facilitate the use of high resolutions. Different boundary conditions can also be easily implemented.

  • Conective instabilities and directional solidification in binary mixtures

     Meca Alvarez, Esteban
    Defense's date: 2010-06-04
    Department of Applied Physics, Universitat Politècnica de Catalunya
    Theses

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  • ESTRUCTURAS COHERENTES Y TURBULENCIA EN DOMINIOS SIMPLES

     Mercader Calvo, Maria Isabel; Avila Cañellas, Marc; Batiste Boleda, Oriol; Meseguer Serrano, Alvaro; Mellibovsky Elstein, Fernando; Panades Guinart, Carles; Alonso Maleta, Maria Aranzazu; López Moscat, Juan Manuel; Marques Truyol, Francisco
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  • Convectons in binary fluid convection: periodic and bounded domains

     Mercader Calvo, Maria Isabel; Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol; Knobloch, Edgar
    International Meeting on Thermodiffusion
    Presentation's date: 2010-06-07
    Presentation of work at congresses

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  • Localized states in binary fluid convection

     Mercader Calvo, Maria Isabel; Knobloch, Edgar; Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol
    Emerging Topics in Dynamical Systems and Partial Differential Equations
    Presentation's date: 2010-05-31
    Presentation of work at congresses

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  • Codimension-2 Bifurcations in Binary-Mixture Convection

     Meca Alvarez, Esteban; Mercader Calvo, Maria Isabel; Ramirez de La Piscina Millan, Laureano
    Emerging Topics in Dynamical Systems and Partial Differential Equations
    Presentation's date: 2010-07-01
    Presentation of work at congresses

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  • Numerical simulation of binary fluid convection near the onset in moderate aspect ratio cylinders

     Alonso Maleta, Maria Aranzazu; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol
    International Meeting on Thermodiffusion
    Presentation's date: 2010-06-07
    Presentation of work at congresses

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  • Transitions between symmetric and non-symmetric flow regimes in a laterally heated binary mixture

     Meca Alvarez, Esteban; Mercader Calvo, Maria Isabel; Ramirez de La Piscina Millan, Laureano
    International Meeting on Thermodiffusion
    Presentation's date: 2010-06-09
    Presentation of work at congresses

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    Localized pinning states in closed containers: homoclinic snaking without bistability  Open access

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2009-08
    Journal article

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    Binary mixtures with a negative separation ratio are known to exhibit time-independent spatially localized convection when heated from below. Numerical continuation of such states in a closed two-dimensional container with experimental boundary conditions and parameter values reveals the presence of a pinning region in Rayleigh number with multiple stable localized states but no bistability between the conduction state and an independent container-filling state. An explanation for this unusual behavior is offered.

  • Convectons in periodic and bounded domains

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    Fluid dynamics research
    Date of publication: 2009-12-21
    Journal article

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    Numerical continuation is used to compute spatially localized convection in a binary fluid with no-slip laterally insulating boundary conditions and the results are compared with the corresponding ones for periodic boundary conditions (PBC). The change in the boundary conditions produces a dramatic change in the snaking bifurcation diagram that describes the organization of localized states with PBC: the snaking branches turn continuously into a large amplitude state that resembles periodic convection with defects at the sidewalls. Odd parity convectons are more affected by the boundary conditions since the sidewalls suppress the horizontal pumping action that accompanies these states in spatially periodic domains.

  • Dinàmica de fluids; formació d'estructures i aplicacions geofísiques

     Marques Truyol, Francisco; Falques Serra, Alberto; Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol; Calvete Manrique, Daniel; Garnier, Roland Charles; Mellibovsky Elstein, Fernando; Mercader Calvo, Maria Isabel; Meseguer Serrano, Alvaro; Pino Gonzalez, David; Ribas Prats, Francesca; van en Berg, Niels; Panades Guinart, Carles
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  • Steady localized states in binary fluid convection: the influence of the boundary condition on the bifurcation diagrams

     Mercader Calvo, Maria Isabel; Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol; Knobloch, Edgar
    Bifurcations and Instabilities in Fluid Dynamics
    Presentation's date: 2009-08-12
    Presentation of work at congresses

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  • Convectons in periodic and bounded domains

     Knobloch, Edgar; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso Maleta, Maria Aranzazu
    62 Annual Meeting of the APS (Division of Fluid Dynamics)
    Presentation's date: 2009-11-22
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  • Spatiotemporal dynamics near the onset of convection for binary mixtures in cylindrical containers

     Mercader Calvo, Maria Isabel; Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2008-01
    Journal article

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  • Spatio-temporal dynamics near the onset of convection in cylindrical containers

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso, A
    Date of publication: 2008-02
    Book chapter

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  • Spatiotemporal dynamics near the onset of convection for binary mixtures in cylindrical containers

     Mercader Calvo, Maria Isabel; Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol
    Physical review E, statistical physics, plasmas, fluids, and related interdisciplinary topics
    Date of publication: 2008-04
    Journal article

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  • Eckhaus instability and homoclinic snaking

     Bergeon, A; Burke, J; Knobloch, Edgar; Mercader Calvo, Maria Isabel
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2008-10
    Journal article

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  • Spatio-temporal dynamics near the onset of convection in cylindrical containers

     Mercader Calvo, Maria Isabel; Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol
    8th International Meeting on Thermodiffusion
    Presentation of work at congresses

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  • Complex dynamics near the onset of convections in sahallow cylinders

     Mercader Calvo, Maria Isabel; Alonso Garcia, Alberto; Batiste Boleda, Oriol
    NoLineal 2008
    Presentation of work at congresses

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  • Spatio-temporal synamics near the onset of convection in cylindrical containers

     Mercader Calvo, Maria Isabel
    8th International Meeting on Thermodiffusion
    Presentation's date: 2008-06-09
    Presentation of work at congresses

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  • Localized steady states in binary fluid convection and their snaking structure

     Batiste Boleda, Oriol; Mercader Calvo, Maria Isabel; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    SIAM Conference on Nonlinear Waves and Coherent Structures
    Presentation of work at congresses

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  • Localized steady in bynary fluid convection and their snaking structure

     Batiste Boleda, Oriol; Mercader Calvo, Maria Isabel; Alonso Garcia, Alberto; Knobloch, Edgar
    SIAM Conference on Nonlinear waves and Coherent Structures
    Presentation of work at congresses

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  • Localized steady states in binary fluid convection ans their snaking structure

     Mercader Calvo, Maria Isabel
    SIAM Conference on Nonlinear Waves and Coherent Structures
    Presentation's date: 2008-07-21
    Presentation of work at congresses

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  • Localized steady states in binary fluid convection

     Batiste Boleda, Oriol; Mercader Calvo, Maria Isabel; Alonso Maleta, Maria Aranzazu; Knobloch, Edgar
    8th International Meeting on Thermodiffusion
    Presentation of work at congresses

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  • Confined steady states in binary fluid convection in rectangular cells

     Batiste Boleda, Oriol; Mercader Calvo, Maria Isabel; Alonso Garcia, Alberto
    NoLineal 2008
    Presentation's date: 2008-06-17
    Presentation of work at congresses

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  • Localized steady states in binary fluid convection

     Mercader Calvo, Maria Isabel
    8th International Meeting on Thermodiffusion
    Presentation's date: 2008-06-09
    Presentation of work at congresses

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  • Localized steady states in binary fluid convection

     Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; Alonso, A
    Date of publication: 2008-02
    Book chapter

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  • Centrifugal effects in rotating convection: Axisymmetric states and three-dimensional instabilities

     Marques Truyol, Francisco; Mercader Calvo, Maria Isabel; Batiste Boleda, Oriol; LOPEZ, J M
    Journal of fluid mechanics
    Date of publication: 2007-06
    Journal article

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  • Numerical simulations of binary fluid convection in large aspect ratio annular containers

     Alonso Maleta, Maria Aranzazu; Batiste Boleda, Oriol; Mercader Calvo, Maria Isabel
    European physical journal. Special topics
    Date of publication: 2007-07
    Journal article

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