L. Corti

Chaotic dynamics in an infinite-dimensional electromagnetic system

The paper deals with bifurcation and chaos phenomena theoretically observed in a simple electromagnetic system consisting of a linear, distortionless transmission line connected to an active linear resistor (R >

A new technique for simulating nonlinear loaded lossy lines

A numerical model for simulating linear lossy transmission lines ended with nonlinear resistors is described. It based on two complementary formulations of the telegraphers equations and uses the Galerkin method. The proposed approach appears computationally less cumbersome than that based on the time-domain convolution method, especially when the analysis of multiconductor transmission lines is considered. Particular attention is paid to the uniqueness of the solution and to the convergence of the numerical approximation. Complementary formulations provide a powerful tool to study the convergence.

Bifurcations and chaos in transmission lines

ContentsIn this article we present some examples of bifurcations and chaotic phenomena theoretically observed in a simple electromagnetic system. The system consists of a linear lossless, or Heaviside distorsionless, transmission line connected to a linear resistor at one end (active branch) and to a nonlinear resistor at the other end (passive branch). The time dynamics of the backward voltage wave evaluated across the nonlinear resistor are described by a one-dimensional non linear mapping. A uniqueness theorem and the discussion of a problem with more than one solution complete the paper.ÜbersichtIn diesem Artikel zeigen wir einige Beispiele von Bifurkationen und chaotischen Phänomenen, die in einfachen elektromagnetischen Systemen theoretisch beobachtet wurden. Das System besteht aus einer linearen verlustfreien oder Heaviside-störungsfreien Übertragungsstrecke, die mit einem linearen Widerstand an einem Ende (aktiver Zweig) und mit einem nichtlinearen Widerstand am anderen Ende (passiver Zweig) verbunden wurde. Das Zeitverhalten der Rückwärtsspannungswelle, das über dem nichtlinearen Widerstand ausgewertet wurde, wird durch eine eindimensionale nichtlineare Abbildung beschrieben. Ein Eineindeutigkeits-Theorem und die Diskussion eines Problems mit mehr als einer Lösung vervollständigen diesen Artikel.

Analogic Realization of a Non-linear Network with Re-configurable Structure as Paradigm for Real Time Analysis of Complex Dynamics

A novel experimental set-up realized for the real time analysis of reconfigurable complex networks, with chaotic Chua’s circuits as nodes, is considered. It has been designed to easily perform large scale experiments on networks of chaotic oscillators, possibly exploring in real time the parameters space in terms of topologies, coupling strengths, nodes’ dynamics, with potential application in the area of neuro-computing and associative dynamic memories. A sample of the capabilities is given by considering diffusive coupling with a large range of coupling strengths in a set of topologies, and first experiments on a ring of 32 chaotic nodes are reported. Synchronization, chaotic waves and patterns are experimentally observed, and the potential of the realized set-up in terms of accuracy, flexibility and analysis time is fully revealed.

Efficient time-domain simulation of lossy multiconductor lines with non-linear loads

The convolution method is applied to analyse lossy multiconductor lines with non-linear loads. The line is described as a time-domain m-port, through the input and transfer impulse responses. A new method is used to evaluate analytically the principal parts of these responses, i.e., the parts containing all the irregular terms, such as Dirac pulses. Once the irregular parts are known, the regular remainders are easily calculated by numerical inversion. The convolution integrals have been evaluated using two different methods, one based on crude trapezoidal rule and the other based on a fast recursive algorithm. The latter is obtained by an exponential fitting of the regular parts of the impulse responses. A comparison between the computation times of these two methods is presented.

An inverse formulation for the identification of magnetic field profiles in plasma lenses

The knowledge and the control of the magnetic field profile is of major importance in the application of plasma discharges as magnetic lenses for charged particle beams, because of the complex dynamics of the plasma. Since conventional field measurements are quite difficult for high current plasma discharges, we propose an inverse formulation for the identification of the field profile directly from the focusing data. The problem is shown to be ill-posed, in general; therefore a regularisation is needed. This is obtained, first, by means of a proper restriction of the observation space; second, by using an overdetermined data set, leading to a pseudo-inversion procedure. The numerical solution is illustrated, showing the procedure to be robust, at least for the practical applications range. In particular it is shown how the proposed method is effective in determining the amount of distortion of the field profile as compared to the reference linear one.

A didactic electronic set-up for introducing to complex networks of chaotic oscillators

The paper describes a portable didactic experiment, realizing a complex network of Chuas circuits, along with its use for introducing collective dynamics in networks of nonlinear oscillators to students. The equipment enables the full configurability of the nodes parameters and the network structure (topology and link impedances). An 8 nodes portable version is realized as a demonstrator, however the corresponding laboratory experiment is designed to be easily scalable to a high number of nodes. The networks control and the data acquisition are automated thanks to a USB interface board and a LabVIEW control interface. The experiment allows the student to perform some direct real time analysis of a set of networked (coupled) Chuas circuits, with the goal to give immediate impact to the discovery of collective behaviors. In particular, the proposed experiences range from the characterization of the complex dynamics of the isolated nodes to the complete synchronization, as well as the emergence of clustering and waves. It is adopted within some course on Advanced Circuit Theory at the Master Degree level.

Time-domain two-port representations of a lossy line

ContentsWe examine the two port representations of a lossy line in the time domain. We give a closed form expression for the canonical responses defining the adopted representation. These expressions are arranged into two contributions: an impulsive term and a regular part. The extension to the multi-conductors case described by Toeplitz, symmetric, and tridiagonal matrices is also discussed.ÜbersichtUntersucht wird die zeitliche Zweitordarstellung einer verlustbehafteten Leitung. Hierzu wird eine geschlossene Beschreibung der kanonischen Impulsantworten, welche zu der obigen Darstellung führen, entwickelt. Diese Beschreibung ist in zwei Beiträge unterteilt: eine Formulierung, der Delta-Verteilungen zu Grunde liegen, und einen stetigen Teil. Darüberhinaus werden auch die Erweiterung bezüglich mehrerer Leitungen (wie von Toeplitz beschrieben) sowie symmetrische und tridiagonale Matrizen behandelt.

Coupling of a nonlinear diffusive electromagnetic system to a linear electric circuit

A composite electromagnetic system that includes a nonhysteretic ferromagnetic conducting body and a linear resonant circuit fed by a sinusoidal voltage source is studied. The diffusion of the magnetic field in the iron core inductor is described by means of a finite-dimensional nonlinear dynamic system obtained by applying the Galerkin method. These equations are coupled with the circuit ones. This physical system might exhibit different nonlinear phenomena: multiple periodic oscillations and even apparently completely disordered aperiodic chaotic motions. Multiple harmonic and subharmonic oscillations are investigated by computer-aided analysis using a static method. >

Dual formulations for error estimation in non‐uniform transmission lines

A time domain discrete model for nonuniform transmission lines, based on a complementary formulation of the transmission line equations, is considered. By recasting the line equations in terms of flux and charge, one has to discretize alternatively only one of the two equations, the other being exactly verified. This approach has been widely used in electromagnetics to evaluate the discretization error. With reference to simple examples, we show how the error estimation can be used for a selective meshing of the line, leading to much better approximation with the same computational effort.