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33
Chaotic Advection in ThreeDimensional Unsteady Incompressible Laminar Flow
, 1996
"... this paper we take advantage of the spherical symmetry of the geometry of this system to y Email julyan@hp1.uib.es, Web http://formentor.uib.es/julyan. ..."
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this paper we take advantage of the spherical symmetry of the geometry of this system to y Email julyan@hp1.uib.es, Web http://formentor.uib.es/julyan.
Simulation of ThreeDimensional BénardMarangoni Flows Including Deformed Surfaces
, 2009
"... We present a coupled thermalfluid model for BénardMarangoni convection in a threedimensional fluid layer. The governing equations are derived in detail for two reasons: first, we do not assume a flat free surface as commonly done; and second, we prepare for the use of flexible discretizations. Th ..."
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We present a coupled thermalfluid model for BénardMarangoni convection in a threedimensional fluid layer. The governing equations are derived in detail for two reasons: first, we do not assume a flat free surface as commonly done; and second, we prepare for the use of flexible discretizations. The governing equations are discretized using spectral elements in space and an operator splitting approach in time. Since we are here primarily interested in steady state solutions, the focus is on the spatial discretization. The overall computational approach is very attractive to use for several reasons: (i) the solution can be expected to have a high degree of regularity, and rapid convergence can be expected; (ii) the spectral element decomposition automatically gives a convenient parameterization of the free surface that allows powerful results from differential geometry to easily be exploited; (iii) free surface deformation can readily be included; (iv) both normal and tangential stresses are conveniently accounted for through a single surface integral; (v) no differentiation of the surface tension is necessary in order to include thermocapillary effects (due to integrationbyparts twice); (vi) the geometry representation of the free surface need only be C 0 across element boundaries even though curvature effects are included. Threedimensional simulation results are presented, including the free surface deflection due to buoyancy and thermocapillary effects.
Two Dimensional DSMC Calculations of the Rayleigh Bénard Instability
, 1996
"... : The Rayleigh B'enard instability is a well known phenomena in which a fluid layer confined between two horizontal, parallel plates heated from below spontaneously initiates convection at some critical temperature difference between the plates. The convective motion takes the form of parallel fluid ..."
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: The Rayleigh B'enard instability is a well known phenomena in which a fluid layer confined between two horizontal, parallel plates heated from below spontaneously initiates convection at some critical temperature difference between the plates. The convective motion takes the form of parallel fluid rolls. A layer of rarefied Helium gas at cryogenic temperatures confined between two plates is simulated in two dimensions by means of the direct simulation Monte Carlo (DSMC) method. The transition from a stable layer to large scale convective motion is simulated. At higher temperature differences some experimentally verified nonlinear phenomena are also observed. The use of the nondimensional heat flux incident on the upper plate is recommended for use when comparing further DSMC studies, as in experiments. Suggestions for further work are also made. 1 INTRODUCTION If a fluid is confined between two horizontal, parallel, perfectly conducting plates and the bottom plate is heated, such...
Stochastic geometry of polygonal networks  an alternative approach to the hexagonsquaretransition in Bénard convection
, 1997
"... The tools of stochastic geometry are applied to the transition from hexagonal to square cells recently observed in surfacetensiondriven Benard convection. By means of this method we study the metrical and topological evolution of Benard cells as a function of the temperature di#erence across the l ..."
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The tools of stochastic geometry are applied to the transition from hexagonal to square cells recently observed in surfacetensiondriven Benard convection. By means of this method we study the metrical and topological evolution of Benard cells as a function of the temperature di#erence across the layer. We find distinct di#erences in the metric of the three cell types. While sidelength, area and perimeter of hexagons and squares grow monotoneously, the particular quantities of the pentagons change with onset of the transition in a steplike manner. Below the transition the pentagons behave similiar to hexagons, above close to squares which underlines their mediating character within the transition. The relation between perimeter and area plays obviously a decisive role for the stability of one cell class. We show that the perimeterarea ratio of a square Benard cell exceeds that of the hexagonal one by an unexpected high value. We find that the Benard pattern obeys to the AboavWeair...
Radiative Transfer in a Static Model Atmosphere
, 2000
"... this paper to give a detailed and definitive analysis of this base state prior to studying the convective instability problem itself. The model chosen is that of a plane parallel layer of grey fluid heated from below. The treatment of the radiation field may be simplified through the adoption of the ..."
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this paper to give a detailed and definitive analysis of this base state prior to studying the convective instability problem itself. The model chosen is that of a plane parallel layer of grey fluid heated from below. The treatment of the radiation field may be simplified through the adoption of the Eddington approximation, which, by comparison with more detailed calculations, can be shown to yield accurate temperature profiles for optically thick layers, even when radiation no longer dominates energy transfer. Variations of the temperature and radiation fields as functions of layer depth are presented and compared with asymptotic formulae obtained under certain restrictive (though practically useful) assumptions. A brief synopsis of the paper follows. x2 sets out the assumptions and simplifications used to derive a model problem suitable for studying the effect of radiative transfer on the mean thermal structure of a fluid layer. x3 derives the governing equations and boundary conditions, both for the Eddington approximation and for a more detailed description of the radiation field. Two dimensionless parameters, the optical depth of the layer and a ratio of radiative to thermal conductivity are shown to characterize the problem. x4 describes the numerical method used to solve the resulting two point boundary problem from x3. x5 presents numerical solutions to these equations, exploring relevant extremes of parameter space. Clear asymptotic behaviour is seen in the results. The Eddington approximation is shown to describe the temperature fields accurately in regions of interest in parameter space. As a consequence, this approximation is analysed to explain the asymptotic behaviour seen in the solutions. x6 presents an analysis for the Eddington approximation based on a...
Scalable Parallel Finite Element Computations of RayleighBenardMarangoni Problems in a Microgravity Environment
"... 1. RayleighBenardMarangoni Flows 1. Microgravity Flow Problems 2. Mathematical Model and Finite element Method 3. Solution Algorithm 4. Parallelization 5. Performance 2. Evaluation Criteria and Performance 3. MGFLO Software Package 1. Code Modules 2. List of Routines 3. Sample Input File 4. Sample ..."
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1. RayleighBenardMarangoni Flows 1. Microgravity Flow Problems 2. Mathematical Model and Finite element Method 3. Solution Algorithm 4. Parallelization 5. Performance 2. Evaluation Criteria and Performance 3. MGFLO Software Package 1. Code Modules 2. List of Routines 3. Sample Input File 4. Sample Output File 5. User specified conditions 6. Usage 4. Test Problem and Performance Results 5. Experimental Studies 6. Conclusions and Recommendations Acknowledgments Glossary References Authors Dr G.F. Carey: project director, professor in Aerospace Engineering at the University of Texas at Austin, director of the CFD Lab. Dr R. Mclay: Research Associate at the University of Texas at Austin. Dr. C. Harlé: Post Doctoral associate, CFD Lab. Dr. B. Davis: Post Doctoral associate, CFD Lab. Dr. H Swinney: Professor at the University of Texas at Austin, director of the Center for Nonlinear Dynamics. Dr. S. Van Hook: Post Doctoral associate, Center for Nonlinear Dynamics. Abstract MGFLO is desi...
Pattern Formation in Solutal Convection: Vermiculated Rolls and Isolated Cells
"... Observations of the peculiar behaviour of a drink of liqueur topped with cream led us to perform experiments showing that the instability is a convection phenomenon that arises through destabilizing surfacetension forces. The convection is solutal: driven by gradients of concentration of a solute, ..."
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Observations of the peculiar behaviour of a drink of liqueur topped with cream led us to perform experiments showing that the instability is a convection phenomenon that arises through destabilizing surfacetension forces. The convection is solutal: driven by gradients of concentration of a solute, rather than by heat gradients as in the more commonly studied thermal convection. The convective patterns, vermiculated rolls and isolated cells, are quite unlike the usual planforms. They are associated with an elastic surface film, and the Marangoni number is high, characteristic of solutal convection. We have conducted further experiments that reproduce these patterns in simpler working fluids.
1.1. The Visual World Paradigm
"... The Visual World Paradigm (VWP) presents listeners with a challenging problem: They must integrate two disparate signals, the spoken language and the visual context, in support of action (e.g., complex movements of the eyes across a scene). We present Impulse Processing, a dynamical systems approach ..."
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The Visual World Paradigm (VWP) presents listeners with a challenging problem: They must integrate two disparate signals, the spoken language and the visual context, in support of action (e.g., complex movements of the eyes across a scene). We present Impulse Processing, a dynamical systems approach to incremental eye movements in the visual world that suggests a framework for integrating language, vision, and action generally. Our approach assumes that impulses driven by the language and the visual context impinge minutely on a dynamical landscape of attractors corresponding to the potential eyemovement behaviors of the system. We test three unique predictions of our approach in an empirical study in the VWP, and describe an implementation in an artificial neural network. We discuss the Impulse Processing framework in relation to other models of the VWP. Keywords: Dynamical systems; Selforganization; Local coherence; Artificial neural networks;
Academic year 20092010Numerical Bifurcation Analysis of Large Scale Systems
"... 1 Classification and wellposedness of PDEs 3 1.1 First order PDEs............................... 3 1.1.1 First order scalar PDEs....................... 3 ..."
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1 Classification and wellposedness of PDEs 3 1.1 First order PDEs............................... 3 1.1.1 First order scalar PDEs....................... 3