Levinson’s theorem, zero‐energy resonances, and time delay in one‐dimensional scattering systems

1994 ◽  
Vol 35 (6) ◽  
pp. 2719-2733 ◽  
Author(s):  
M. Sassoli de Bianchi
Keyword(s):  
Time Delay ◽  
Zero Energy ◽  
One Dimensional ◽  
Levinson’S Theorem ◽  
Scattering Systems

scholarly journals Topological phase transition between a normal insulator and a topological metal state in a quasi-one-dimensional system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Milad Jangjan ◽  
Mir Vahid Hosseini
Keyword(s):  
Phase Transition ◽  
Dimensional System ◽  
Inversion Symmetry ◽  
Topological Phase ◽  
Edge States ◽  
Zero Energy ◽  
One Dimensional ◽  
Topological Phase Transition ◽  
Metal State ◽  
Topological Metal

AbstractWe theoretically report the finding of a new kind of topological phase transition between a normal insulator and a topological metal state where the closing-reopening of bandgap is accompanied by passing the Fermi level through an additional band. The resulting nontrivial topological metal phase is characterized by stable zero-energy localized edge states that exist within the full gapless bulk states. Such states living on a quasi-one-dimensional system with three sublattices per unit cell are protected by hidden inversion symmetry. While other required symmetries such as chiral, particle-hole, or full inversion symmetry are absent in the system.

Research on Parallel PZT Phased Array Based Structural Health Monitoring in CFPR

2013 ◽  
Vol 753-755 ◽  
pp. 2343-2346
Author(s):  
Ya Jie Sun ◽  
Yong Hong Zhang ◽  
Hui Qiang Tang ◽  
Cheng Shan Qian ◽  
Shen Fang Yuan
Keyword(s):  
Time Delay ◽  
Structural Health Monitoring ◽  
Health Monitoring ◽  
Lamb Wave ◽  
Phased Array ◽  
Signal Amplitude ◽  
Gray Scale ◽  
One Dimensional ◽  
Structural Health ◽  
Damage Location

Phased array theroy can controll the Lamb wave beem steering in certain range by adding the time delay to the signals. Phased array theory is used to identify the damge in the structure. One dimensional PZT array is restricted in monitoring distance. Two parellel PZT sensors arrays are utilized to monitor the CFPR structure to extend the monitoring distance and to improve the precision of the damage locatilization. The experiment is done on the CFPR structure by using two parellel PZT arrays to detect the damage in the structure. The results of the experiment is shown on the mapped image. Gray-scale in the mapped image from dark to light corresponds to the signal amplitude from low to high. The highlight of the mapped image is the damage location in the structure. The monitoring results in the CFPR structure by two parellel PZT arrays is accurate and identical.

scholarly journals Finite-size effects on topological interface states in one-dimensional scattering systems

2018 ◽  
Vol 98 (2) ◽  
Author(s):  
P. A. Kalozoumis ◽  
G. Theocharis ◽  
V. Achilleos ◽  
S. Félix ◽  
O. Richoux ◽  
...  
Keyword(s):  
Size Effects ◽  
Finite Size ◽  
Interface States ◽  
Finite Size Effects ◽  
One Dimensional ◽  
Scattering Systems

Stability results for an elastic–viscoelastic wave equation with localized Kelvin–Voigt damping and with an internal or boundary time delay

2020 ◽  
pp. 1-57
Author(s):  
Mouhammad Ghader ◽  
Rayan Nasser ◽  
Ali Wehbe
Keyword(s):  
Wave Equation ◽  
Time Delay ◽  
Frequency Domain ◽  
Viscoelastic Damping ◽  
One Dimensional ◽  
Viscoelastic Wave ◽  
Smooth Coefficients ◽  
The Stability ◽  
Stability Results ◽  
Dimensional Wave

We investigate the stability of a one-dimensional wave equation with non smooth localized internal viscoelastic damping of Kelvin–Voigt type and with boundary or localized internal delay feedback. The main novelty in this paper is that the Kelvin–Voigt and the delay damping are both localized via non smooth coefficients. Under sufficient assumptions, in the case that the Kelvin–Voigt damping is localized faraway from the tip and the wave is subjected to a boundary delay feedback, we prove that the energy of the system decays polynomially of type t − 4 . However, an exponential decay of the energy of the system is established provided that the Kelvin–Voigt damping is localized near a part of the boundary and a time delay damping acts on the second boundary. While, when the Kelvin–Voigt and the internal delay damping are both localized via non smooth coefficients near the boundary, under sufficient assumptions, using frequency domain arguments combined with piecewise multiplier techniques, we prove that the energy of the system decays polynomially of type t − 4 . Otherwise, if the above assumptions are not true, we establish instability results.

THE EFFECT OF TIME DELAY ON SPATIOTEMPORAL DYNAMICS IN ONE-DIMENSIONAL DISCRETE EXCITABLE MEDIA

2001 ◽  
Vol 15 (02) ◽  
pp. 167-176
Author(s):  
TAE-HOON CHUNG ◽  
SEUNGWHAN KIM
Keyword(s):  
Time Delay ◽  
Spatiotemporal Dynamics ◽  
Excitable Media ◽  
Winding Number ◽  
One Dimensional ◽  
Circle Maps ◽  
Pattern Complexity ◽  
Existence And Stability ◽  
Spatiotemporal Intermittency ◽  
The Stability

We investigate the effect of time delay on spatiotemporal dynamics in one-dimensional discrete excitable media with local delayed-interactions using coupled sine circle-maps. With the help of the stability analysis and numerical calculation of the pattern complexity entropy, we construct the phase diagram in the parameter space time delay and the nonlinear coupling. We find that the time delay affects the existence and stability of various regular states including homogeneously phase-locked and checkerboard states. In particular, the time delay induces the breakup of the homogeneously phase-locked state into spatiotemporal intermittency and the occurrence of multi-stability that depends on the winding number.

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