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Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
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Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation
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Bifurcation to fronts due to delay.

T Erneux1, G Kozyreff, M Tlidi

  • 1Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Campus Plaine, CP 231, 1050 Bruxelles, Belgium. terneux@ulb.ac.be

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 17, 2009
PubMed
Summary
This summary is machine-generated.

This study investigates how time-delayed feedback control affects front stability. We found that delayed feedback can induce front movement and determined conditions for propagation in 2D systems.

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Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Physics
  • Control Theory

Background:

  • Steady-state fronts, or kinks, are fundamental in various physical and biological systems.
  • Controlling front dynamics is crucial for applications ranging from pattern formation to reaction-diffusion processes.
  • Time-delayed feedback control (TDFC) offers a unique method to influence system behavior by incorporating past states.

Purpose of the Study:

  • To analyze the stability of a steady-state front under time-delayed feedback control (TDFC).
  • To investigate the emergence of moving fronts and their propagation dynamics.
  • To determine the conditions for propagation in two-dimensional systems with radial symmetry.

Main Methods:

  • Mathematical analysis of front stability with TDFC.
  • Bifurcation analysis to identify transitions to moving fronts.
  • Investigation of asymptotic limits for large delays and weak feedback.
  • Examination of a two-dimensional radially symmetric front model.

Main Results:

  • Demonstrated the existence of a bifurcation leading to a moving front under TDFC.
  • Derived a global bifurcation diagram for propagation speed in the limit of large delays and weak feedback.
  • Identified the critical radius for propagation in two-dimensional radially symmetric fronts.

Conclusions:

  • TDFC can destabilize steady-state fronts, inducing motion.
  • The propagation speed of fronts is controllable and predictable through bifurcation analysis.
  • Radial symmetry plays a critical role in determining propagation possibility in 2D systems.