9,149 research outputs found
Structural transition in interdependent networks with regular interconnections
Networks are often made up of several layers that exhibit diverse degrees of
interdependencies. A multilayer interdependent network consists of a set of
graphs that are interconnected through a weighted interconnection matrix , where the weight of each inter-graph link is a non-negative real number . Various dynamical processes, such as synchronization, cascading failures
in power grids, and diffusion processes, are described by the Laplacian matrix
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 , being the identity matrix, it has
been shown that there exists a structural transition at some critical coupling,
. This transition is such that dynamical processes are separated into
two regimes: if , the network acts as a whole; whereas when , the network operates as if the graphs encoding the layers were isolated. In
this paper, we extend and generalize the structural transition threshold to a regular interconnection matrix (constant row and column sum).
Specifically, we provide upper and lower bounds for the transition threshold in interdependent networks with a regular interconnection matrix
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 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
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
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
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
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
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Matrix pencil representation of structural transformations of passive electrical networks
The paper examines the problem of systems redesign within the context of passive electrical networks by considering the problem of multi-parameter and topology changes, and their representation. This representation may be used to investigate the impact of such changes on properties such as characteristic frequencies. The general problem area is the modelling of systems, whose structure is not fixed but evolves during the system life-cycle. The specific problem we are addressing is the study of effect of changing the topology of an electrical network that is changing individual elements of the network into elements of different type and value, augmenting / or eliminating parts of the network and developing a framework that allows the study of the effect of such transformations on the natural frequencies. This problem is a special case of the more general network redesign problem. We use the Impedance-Admittance models and we establish a representation of the different types of transformations on such models. The representation of the structural transformations is given in terms of the companion pencil that preserves the natural topologies of the RLC network
A digital computer program for the dynamic interaction simulation of controls and structure (DISCOS), volume 1
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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