9,149 research outputs found

    Structural transition in interdependent networks with regular interconnections

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    Networks are often made up of several layers that exhibit diverse degrees of interdependencies. A multilayer interdependent network consists of a set of graphs GG that are interconnected through a weighted interconnection matrix B B , where the weight of each inter-graph link is a non-negative real number p p . Various dynamical processes, such as synchronization, cascading failures in power grids, and diffusion processes, are described by the Laplacian matrix Q Q characterizing the whole system. For the case in which the multilayer graph is a multiplex, where the number of nodes in each layer is the same and the interconnection matrix B=pI B=pI , being I I the identity matrix, it has been shown that there exists a structural transition at some critical coupling, p∗ p^* . This transition is such that dynamical processes are separated into two regimes: if p>p∗ p > p^* , the network acts as a whole; whereas when p<p∗ p<p^* , the network operates as if the graphs encoding the layers were isolated. In this paper, we extend and generalize the structural transition threshold p∗ p^* to a regular interconnection matrix B B (constant row and column sum). Specifically, we provide upper and lower bounds for the transition threshold p∗ p^* in interdependent networks with a regular interconnection matrix B B and derive the exact transition threshold for special scenarios using the formalism of quotient graphs. Additionally, we discuss the physical meaning of the transition threshold p∗ p^* in terms of the minimum cut and show, through a counter-example, that the structural transition does not always exist. Our results are one step forward on the characterization of more realistic multilayer networks and might be relevant for systems that deviate from the topological constrains imposed by multiplex networks.Comment: 13 pages, APS format. Submitted for publicatio

    System Level Synthesis

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    This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

    Damping characterization in large structures

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    This research project has as its main goal the development of methods for selecting the damping characteristics of components of a large structure or multibody system, in such a way as to produce some desired system damping characteristics. The main need for such an analytical device is in the simulation of the dynamics of multibody systems consisting, at least partially, of flexible components. The reason for this need is that all existing simulation codes for multibody systems require component-by-component characterization of complex systems, whereas requirements (including damping) often appear at the overall system level. The main goal was met in large part by the development of a method that will in fact synthesize component damping matrices from a given system damping matrix. The restrictions to the method are that the desired system damping matrix must be diagonal (which is almost always the case) and that interbody connections must be by simple hinges. In addition to the technical outcome, this project contributed positively to the educational and research infrastructure of Tuskegee University - a Historically Black Institution

    A bibliography on parallel and vector numerical algorithms

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    This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

    Constrained Texture Mapping And Foldover-free Condition

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    Texture mapping has been widely used in image processing and graphics to enhance the realism of CG scenes. However to perfectly match the feature points of a 3D model with the corresponding pixels in texture images, the parameterisation which maps a 3D mesh to the texture space must satisfy the positional constraints. Despite numerous research efforts, the construction of a mathematically robust foldover-free parameterisation subject to internal constraints is still a remaining issue. In this paper, we address this challenge by developing a two-step parameterisation method. First, we produce an initial parameterisation with a method traditionally used to solve structural engineering problems, called the bar-network. We then derive a mathematical foldover-free condition, which is incorporated into a Radial Basis Function based scheme. This method is therefore able to guarantee that the resulting parameterization meets the hard constraints without foldovers

    A digital computer program for the dynamic interaction simulation of controls and structure (DISCOS), volume 1

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    A theoretical development and associated digital computer program system for the dynamic simulation and stability analysis of passive and actively controlled spacecraft are presented. The dynamic system (spacecraft) is modeled as an assembly of rigid and/or flexible bodies not necessarily in a topological tree configuration. The computer program system is used to investigate total system dynamic characteristics, including interaction effects between rigid and/or flexible bodies, control systems, and a wide range of environmental loadings. In addition, the program system is used for designing attitude control systems and for evaluating total dynamic system performance, including time domain response and frequency domain stability analyses
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