The state-variable approach to network analysis

Kuh, E.S.; Rohrer, R.A.

doi:10.1109/proc.1965.3991

Cited by 212 publications

(57 citation statements)

References 17 publications

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“…As for the theoretical aspects pointed out in the introduction to this section, bridging region compatibility is relevant to ensure the well posedness of each subdomain problem. In fact, in terms of network analysis it guarantees that the simple State Variable solution approach described in [104] can be pursued, since it implies the absence of capacitance loops and inductance cut sets. In mathematical terms, 0D models are described by Differential Algebraic Systems (DAE) of equations and bridging region compatibility guarantees that the system is of type 1 [6], so it reduces to a standard system of ODE.…”

Section: End Domentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

166

157

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This review paper addresses the so called geometric multiscale approach for the numerical simulation of blood flow problems, from its origin (that we can collocate in the second half of '90s) to our days. By this approach the blood fluid-dynamics in the whole circulatory system is described mathematically by means of heterogeneous featuring different degree of detail and different geometric dimension that interact together through appropriate interface coupling conditions.Our review starts with the introduction of the stand-alone problems, namely the 3D fluidstructure interaction problem, its reduced representation by means of 1D models, and the so-called lumped parameters (aka 0D) models, where only the dependence on time survives. We then address specific methods for stand-alone 3D models when the available boundary data are not enough to ensure the mathematical well posedness. These so-called "defective problems" naturally arise in practical applications of clinical relevance but also because of the interface coupling of heterogeneous problems that are generated by the geometric multiscale process. We also describe specific issues related to the boundary treatment of reduced models, particularly relevant to the geometric multiscale coupling. Next, we detail the most popular numerical algorithms for the solution of the coupled problems. Finally, we review some of the most representative works -from different research groups -which addressed the geometric multiscale approach in the past years.A proper treatment of the different scales relevant to the hemodynamics and their interplay is essential for the accuracy of numerical simulations and eventually for their clinical impact. This paper aims at providing a state-of-the-art picture of these topics, where the gap between theory and practice demands rigorous mathematical models to be reliably filled.

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Section: End Domentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

166

157

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“…matrix, P 2 is n 2 x n 2 p.s.d. matrix, then n 1 ≤ rank P < n, "t Є T. (c) The SSS (1) appearst in the process of modelling of LTV RLC networks [8][9][10][11].…”

Section: Assumptionmentioning

confidence: 99%

Bibo Stability of a Class of Linear Time‐variable Semi‐state Systems and Application in the Analysis of RLC Electrical Networks

Bajić

1987

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.

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“…The encapsulation and mount equivalent circuit have been evaluated using the spprosirnate method due to Getsinger (1966). By considering as variables thc capacitor voltages and inductor currents the behaviour of the microwave cavity equivalent circuit may be expressed using a set of state equations (Kuh and Rohrer 1965). These may be combined with the diode equations to produce a matrix state equation for the diode-cavity configuration, of form :…”

Section: Read Diode Coaxial Oscillatormentioning

confidence: 99%

Small signal lumped model for IMPATT diodes†

Stewart

Conn

Mitchell

1970

International Journal of Electronics

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A small signal lumped model of a general IMPATT diode is presented. By applying state space analysis techniques the model is used to predict the small signal impedance of both pn and pin IMPATT diodes as a function of frequency and d.c. bias current. A lumped element equivalent circuit for the microwave cavity in a Read diode coaxial oscillator is derived. Using a state space description of the diode-cavity configuration, the variation of small signal oscillation frequency with d.c. bias current is evaluated.

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The state-variable approach to network analysis

Cited by 212 publications

References 17 publications

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Bibo Stability of a Class of Linear Time‐variable Semi‐state Systems and Application in the Analysis of RLC Electrical Networks

Small signal lumped model for IMPATT diodes†

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