108,983 research outputs found

    Two-dimensional global manifolds of vector fields

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    We describe an efficient algorithm for computing two-dimensional stable and unstable manifolds of three-dimensional vector fields. Larger and larger pieces of a manifold are grown until a sufficiently long piece is obtained. This allows one to study manifolds geometrically and obtain important features of dynamical behavior. For illustration, we compute the stable manifold of the origin spiralling into the Lorenz attractor, and an unstable manifold in zeta(3)-model converging to an attracting limit cycle

    Locally optimal controllers and globally inverse optimal controllers

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    In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing a LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem

    On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations

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    The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for coarse spatial resolutions and small time step sizes. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.Comment: 31 page

    Object oriented design of a thermo-mechanical FEM code

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    An object oriented design is presented for a computer program that can perform\ud thermo-mechanically coupled analyzes. The target of the design is a \ud exible and robust\ud computer program. It should be easy to adapt and extend, re-using existing code, without\ud interfering with already established algorithms.\ud The program uses publicly available toolkits that are currently emerging as C++ pack-\ud ages. First of all the Standard C++ Library (formerly Standard Template Library) is\ud used for packing items in container classes. Secondly the matrix and vector operations\ud are derived from the Template Numerical Toolkit (TNT) and �nally (not essentially for\ud the numerical part) a graphical user interface is made, based on the wxWindows package,\ud that can generate a GUI for Motif and MS-Windows with the same code.\ud Attention is given to the design of classes such as speci�c elements and material classes\ud based on more general classes. A hierarchy of classes is constructed where general behavior\ud is put high in the hierarchy and speci�c behavior low. The choice between inheritance and\ud aggregation is made at several levels

    Fluctuations of elastic interfaces in fluids: Theory and simulation

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    We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a numerical method, we first discuss the dynamical coupling between the interface and the surrounding fluids. An argument is then presented that generalizes the single-relaxation time lattice-Boltzmann method for the simulation of hydrodynamic interfaces to include the elastic properties of the boundary. The implementation of the new method is outlined and it is tested by simulating the static behavior of spherical bubbles and the dynamics of bending waves. By means of the fluctuation-dissipation theorem we recover analytically the equilibrium frequency power spectrum of thermally fluctuating membranes and the correlation function of the excitations. Also, the non-equilibrium scaling properties of the membrane roughening are deduced, leading us to formulate a scaling law describing the interface growth, W^2(L,T)=L^3 g[t/L^(5/2)], where W, L and T are the width of the interface, the linear size of the system and the temperature respectively, and g is a scaling function. Finally, the phenomenology of thermally fluctuating membranes is simulated and the frequency power spectrum is recovered, confirming the decay of the correlation function of the fluctuations. As a further numerical study of fluctuating elastic interfaces, the non-equilibrium regime is reproduced by initializing the system as an interface immersed in thermally pre-excited fluids.Comment: 15 pages, 11 figure

    On the use of local max-ent shape functions for the simulation of forming processes

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    In this work we review the opportunities given by the use of local maximum-\ud entropy approximants (LME) for the simulation of forming processes. This approximation can\ud be considered as a meshless approximation scheme, and thus presents some appealing features\ud for the numerical simulation of forming processes in a Galerkin framework.\ud Especially the behavior of these shape functions at the boundary is interesting. At nodes\ud on the boundary, the functions possess a weak Kronecker-delta property, hence simplifying the\ud prescription of boundary conditions. Shape functions at the boundary do not overlap internal\ud nodes, nor do internal shape functions overlap nodes at the boundary. Boundary integrals can be\ud computed easily and efficiently compared to for instance moving least-squares approximations.\ud Furthermore, LME shapes also present a controllable degree of smoothness.\ud To test the performance of the LME shapes, an elastic and a elasto-plastic problem was\ud analyzed. The results were compared with a meshless method based on a moving least-squares\ud approximation

    A Mixed Eulerian-Lagrangian Model for the Analysis of Dynamic Fracture

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    National Science Foundation Grant MEA 84-0065

    The basic ingredients of the North Atlantic storm track. Part I: land-sea contrast and orography

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    Understanding and predicting changes in storm tracks over longer time scales is a challenging problem, particularly in the North Atlantic. This is due in part to the complex range of forcings (land–sea contrast, orography, sea surface temperatures, etc.) that combine to produce the structure of the storm track. The impact of land–sea contrast and midlatitude orography on the North Atlantic storm track is investigated through a hierarchy of GCM simulations using idealized and “semirealistic” boundary conditions in a high-resolution version of the Hadley Centre atmosphere model (HadAM3). This framework captures the large-scale essence of features such as the North and South American continents, Eurasia, and the Rocky Mountains, enabling the results to be applied more directly to realistic modeling situations than was possible with previous idealized studies. The physical processes by which the forcing mechanisms impact the large-scale flow and the midlatitude storm tracks are discussed. The characteristics of the North American continent are found to be very important in generating the structure of the North Atlantic storm track. In particular, the southwest–northeast tilt in the upper tropospheric jet produced by southward deflection of the westerly flow incident on the Rocky Mountains leads to enhanced storm development along an axis close to that of the continent’s eastern coastline. The approximately triangular shape of North America also enables a cold pool of air to develop in the northeast, intensifying the surface temperature contrast across the eastern coastline, consistent with further enhancements of baroclinicity and storm growth along the same axis
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