702 research outputs found

    Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities

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    We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model recently developed by Abels, Garcke, and Gr\"un for fluids with different densities, which leads to a solenoidal velocity field. The model is given by a non-homogeneous Navier-Stokes system with a modified convective term coupled to a Cahn-Hilliard system. The density of the mixture depends on an order parameter.Comment: 33 page

    Linear semigroups with coarsely dense orbits

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    Let SS be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space VV. We show that every coarsely dense orbit of SS is actually dense in VV. More generally, if the orbit contains a coarsely dense subset of some open cone CC in VV then the closure of the orbit contains the closure of CC. In the complex case the orbit is then actually dense in VV. For the real case we give precise information about the possible cases for the closure of the orbit.Comment: We added comments and remarks at various places. 14 page

    Large Time Existence for Thin Vibrating Plates

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    We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as h0h\to 0 is either the nonlinear von K\'arm\'an plate equation or the linear fourth order Germain-Lagrange equation. In the case of the linear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation

    Grain-size characterization of reworked fine-grained aeolian deposits

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    After a previous review of the grain-size characteristics of in situ (primary) fine-grained aeolian deposits, reworked (secondary) aeolian deposits, as modified in lacustrine environments and by alluvial and pedogenic processes, are discussed in this paper. As a reference, the grain-size characteristics of primary loess deposits are shortly described. Commonly, pedogenesis and weathering of primary loess may lead to clay neoformation and thus to an enrichment in grain diameters of 4-8 mu m, a size which is comparable to the fine background loess. Remarkably, the modal grain-size values of primary loess are preserved after re -deposition in lakes and flood plains. But, secondary lacustrine settings show a very characteristic admixture with a clayey population of 1-2,5 mu m diameter due to the process of settling in standing water. Similarly, alluvial settings show often an addition with coarse-grained sediment supplied by previously eroded sediment. However, floodplain settings show also often the presence of pools and other depressions which behave similarly to lacustrine environments. As a result, alluvial secondary loess sediments are characterized by the poorest grain-size sorting when compared with the other secondary loess and primary loess. Despite the characteristic texture of each of these deposits, grain-size characteristics of the described individual sediment categories are not always fully diagnostic and thus grain-size analysis should be complemented by other information, as sedimentary structures and fauna or flora, to reliably reconstruct the sedimentary processes and environments

    POD for optimal control of the Cahn-Hilliard system using spatially adapted snapshots

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    The present work considers the optimal control of a convective Cahn-Hilliard system, where the control enters through the velocity in the transport term. We prove the existence of a solution to the considered optimal control problem. For an efficient numerical solution, the expensive high-dimensional PDE systems are replaced by reduced-order models utilizing proper orthogonal decomposition (POD-ROM). The POD modes are computed from snapshots which are solutions of the governing equations which are discretized utilizing adaptive finite elements. The numerical tests show that the use of POD-ROM combined with spatially adapted snapshots leads to large speedup factors compared with a high-fidelity finite element optimization

    Coercivity and stability results for an extended Navier-Stokes system

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    In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained L2L^2 energy estimate. However, through use of new H1H^1 coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

    Augmented reality-based remote family visits in nursing homes

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    During the COVID-19 pandemic, many nursing homes had to restrict visitations. This had a major negative impact on the wellbeing of residents and their family members. In response, residents and family members increasingly resorted to mediated communication to maintain social contact. To facilitate high-quality mediated social contact between residents in nursing homes and remote family members, we developed an augmented reality (AR)-based communication tool. In this study, we compared the user experience (UX) of AR-communication with that of video calling, for 10 pairs of residents and family members. We measured enjoyment, spatial presence and social presence, attitudes, behavior and conversation duration. In the AR-communication condition, residents perceived a 3D projection of their remote family member onto a chair placed in front of them. In the video calling condition, the family member was shown using 2D video. In both conditions, the family member perceived the resident in the video calling mode on a 2D screen. While residents reported no differences in their UX between both conditions, family members reported higher spatial presence for the AR-communication condition compared to video-calling. Conversation durations were significantly longer during AR-communication than during video calling. We tentatively suggest that there may be (unconscious) differences in UX during AR-based communication compared to video calling

    The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

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    We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments
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