31,450 research outputs found

    On the linear stability of K\"ahler-Ricci solitons

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    This is a short note proving that K\"ahler-Ricci solitons with dimH(1,1)(M)2\dim H^{(1,1)}(M)\ge 2 are linearly unstable. This extends the results of Cao-Hamilton-Ilmanen in the K\"ahler-Einstein case.Comment: 11 pages; typos corrected, presentation improved and references added in v.

    Projective vs metric structures

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    We present a number of conditions which are necessary for an n-dimensional projective structure (M,[nabla]) to include the Levi-Civita connection nabla of some metric on M. We provide an algorithm, which effectively checks if a Levi-Civita connection is in the projective class and, in the positive, which finds this connection and the metric. The article also provides a basic information on invariants of projective structures, including the treatment via Cartan's normal projective connection. In particular we show that there is a number of Fefferman-like conformal structures, defined on a subbundle of the Cartan bundle of the projective structure, which encode the projectively invariant information about (M,[nabla])

    Offshore Turbine Arrays: Numerical Modeling and Experimental Validation

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    The interaction between wind turbines in a large wind farm needs to be better understood to reduce array losses and improve energy production. A numerical test bed for an array of offshore wind turbines was developed in the open-source computational fluid dynamics (CFD) framework OpenFOAM. It provides a computational tool which can be used in combination with physical model turbine array studies in the Flow Physics Facility (FPF) at UNH as well as other test facilities. Turbines were modeled as actuator disks with turbulence sources to reduce computational cost. Both k-ϵ and k-ω SST turbulence models were utilized to capture the flow in the near-wall, wake, and free stream regions. Experimental studies were performed in the FPF to validate the numerical results and to provide realistic initial and boundary conditions, for example turbulent boundary layer inlet velocity profiles. Mesh refinement and boundary condition studies were performed. Numerical simulations were executed on a custom-built server, designed to be the head node of a future CFD cluster. The entire project was built on open-source software to facilitate replication and expansion. The numerical model provides building blocks for simulations of large wind turbine arrays, computational resources permitting. The numerical model currently replicates a three by one array of wind turbines in the FPF, and provides detailed insight into the array fluid dynamics
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