6,942 research outputs found

    Vertex Fault Tolerant Additive Spanners

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    A {\em fault-tolerant} structure for a network is required to continue functioning following the failure of some of the network's edges or vertices. In this paper, we address the problem of designing a {\em fault-tolerant} additive spanner, namely, a subgraph HH of the network GG such that subsequent to the failure of a single vertex, the surviving part of HH still contains an \emph{additive} spanner for (the surviving part of) GG, satisfying dist(s,t,H∖{v})≤dist(s,t,G∖{v})+βdist(s,t,H\setminus \{v\}) \leq dist(s,t,G\setminus \{v\})+\beta for every s,t,v∈Vs,t,v \in V. Recently, the problem of constructing fault-tolerant additive spanners resilient to the failure of up to ff \emph{edges} has been considered by Braunschvig et. al. The problem of handling \emph{vertex} failures was left open therein. In this paper we develop new techniques for constructing additive FT-spanners overcoming the failure of a single vertex in the graph. Our first result is an FT-spanner with additive stretch 22 and O~(n5/3)\widetilde{O}(n^{5/3}) edges. Our second result is an FT-spanner with additive stretch 66 and O~(n3/2)\widetilde{O}(n^{3/2}) edges. The construction algorithm consists of two main components: (a) constructing an FT-clustering graph and (b) applying a modified path-buying procedure suitably adopted to failure prone settings. Finally, we also describe two constructions for {\em fault-tolerant multi-source additive spanners}, aiming to guarantee a bounded additive stretch following a vertex failure, for every pair of vertices in S×VS \times V for a given subset of sources S⊆VS\subseteq V. The additive stretch bounds of our constructions are 4 and 8 (using a different number of edges)

    Methods for comparative evaluation of propulsion system designs for supersonic aircraft

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    The propulsion system comparative evaluation study was conducted to define a rapid, approximate method for evaluating the effects of propulsion system changes for an advanced supersonic cruise airplane, and to verify the approximate method by comparing its mission performance results with those from a more detailed analysis. A table look up computer program was developed to determine nacelle drag increments for a range of parametric nacelle shapes and sizes. Aircraft sensitivities to propulsion parameters were defined. Nacelle shapes, installed weights, and installed performance was determined for four study engines selected from the NASA supersonic cruise aircraft research (SCAR) engine studies program. Both rapid evaluation method (using sensitivities) and traditional preliminary design methods were then used to assess the four engines. The method was found to compare well with the more detailed analyses

    Breakdown of disordered media by surface loads

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    We model an interface layer connecting two parts of a solid body by N parallel elastic springs connecting two rigid blocks. We load the system by a shear force acting on the top side. The springs have equal stiffness but are ruptured randomly when the load reaches a critical value. For the considered system, we calculate the shear modulus, G, as a function of the order parameter, \phi, describing the state of damage, and also the ``spalled'' material (burst) size distribution. In particular, we evaluate the relation between the damage parameter and the applied force and explore the behaviour in the vicinity of material breakdown. Using this simple model for material breakdown, we show that damage, caused by applied shear forces, is analogous to a first-order phase transition. The scaling behaviour of G with \phi is explored analytically and numerically, close to \phi=0 and \phi=1 and in the vicinity of \phi_c, when the shear load is close but below the threshold force that causes material breakdown. Our model calculation represents a first approximation of a system subject to wear induced loads.Comment: 15 pages, 7 figure

    A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D

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    A direct reconstruction algorithm for complex conductivities in W2,∞(Ω)W^{2,\infty}(\Omega), where Ω\Omega is a bounded, simply connected Lipschitz domain in R2\mathbb{R}^2, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.Comment: This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0266-5611/28/9/09500

    Derating a single wind farm turbine for reducing its wake and fatigue

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    Derating of individual turbines is one of the options to implement wind farm performance optimization, although there are different ways to proceed with such derating at the turbine control level. The present paper develops an option based on the minimal thrust coefficient in accordance with the Cp and C t contour levels. This strategy is compared for the region below rated wind speed with two other strategies where either the pitch or the tip speed ratio are maintained at their maximum C p values from normal operation. The study concludes that maintaining the pitch at the optimal value from normal operation produces poorer performance from the thrust and the loads perspective. Practical implementation issues have also been detected
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