Two-dimensional linear modes and solitons in parity-time symmetry bessel complex-valued potential

2015 ◽  
Vol 355 ◽  
pp. 50-57 ◽  
Author(s):  
Haibo Chen ◽  
Sumei Hu
Keyword(s):  
Two Dimensional ◽  
Time Symmetry ◽  
Complex Valued

Two-dimensional solitons in triangular photonic lattices with parity-time symmetry

2015 ◽  
Vol 335 ◽  
pp. 146-152 ◽  
Author(s):  
Hong Wang ◽  
Shuang Shi ◽  
Xiaoping Ren ◽  
Xing Zhu ◽  
Boris A. Malomed ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Photonic Lattices ◽  
Time Symmetry

Spatio-temporal dynamics of a periodically driven cavity flow

2003 ◽  
Vol 478 ◽  
pp. 197-226 ◽  
Author(s):  
M. J. VOGEL ◽  
A. H. HIRSA ◽  
J. M. LOPEZ
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Three Dimensional ◽  
Spanwise Direction ◽  
Two Dimensional ◽  
Measured Velocity ◽  
Time Symmetry ◽  
Time Flow ◽  
Time Periodic

The flow in a rectangular cavity driven by the sinusoidal motion of the floor in its own plane has been studied both experimentally and computationally over a broad range of parameters. The stability limits of the time-periodic two-dimensional base state are of primary interest in the present study, as it is within these limits that the flow can be used as a viable surface viscometer (as outlined theoretically in Lopez & Hirsa 2001). Three flow regimes have been found experimentally in the parameter space considered: an essentially two-dimensional time-periodic flow, a time-periodic three-dimensional flow with a cellular structure in the spanwise direction, and a three-dimensional irregular (in both space and time) flow. The system poses a space–time symmetry that consists of a reflection about the vertical mid-plane together with a half-period translation in time (RT symmetry); the two-dimensional base state is invariant to this symmetry. Computations of the two-dimensional Navier–Stokes equations agree with experimentally measured velocity and vorticity to within experimental uncertainty in parameter regimes where the flow is essentially uniform in the spanwise direction, indicating that in this cavity with large spanwise aspect ratio, endwall effects are small and localized for these cases. Two classes of flows have been investigated, one with a rigid no-slip top and the other with a free surface. The basic states of these two cases are quite similar, but the free-surface case breaks RT symmetry at lower forcing amplitudes, and the structure of the three-dimensional states also differs significantly between the two classes.

Defect solitons in two-dimensional photonic lattices with parity-time symmetry

2014 ◽  
Vol 313 ◽  
pp. 139-145 ◽  
Author(s):  
Jianing Xie ◽  
Zhikun Su ◽  
Weicheng Chen ◽  
Guojie Chen ◽  
Jiantao Lv ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Photonic Lattices ◽  
Time Symmetry

SPATIAL, TEMPORAL, AND GLOBAL MODE ENTROPY IN A THALAMO–CORTICAL NETWORK

1993 ◽  
Vol 03 (06) ◽  
pp. 1487-1501 ◽  
Author(s):  
GENE V. WALLENSTEIN
Keyword(s):  
Cortical Neurons ◽  
Space Time ◽  
Time Behavior ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Cortical Cells ◽  
Global Mode ◽  
Time Symmetry ◽  
Symmetry Properties ◽  
Cortical System

We employ an orthogonal decomposition technique with unique space–time symmetry properties to analyze a network of thalamo–cortical oscillators. A small number of thalamic "cells" are used to drive a network of cortical cells structured on a two-dimensional lattice. Two Bonhoeffer–van der Pol (BVP) based models of cortical neurons are compared at the network level in an attempt to reproduce some features of the thalamo–cortical system. It is shown that with the addition of a slowly varying term to the classical two-dimensional BVP model, the network can exhibit both periodic and irregular space–time behavior, along with changes in the temporal coherence and spatial frequency resembling the 8–12 Hz alpha rhythm.

scholarly journals Imaging of complex-valued tensors for two-dimensional Maxwell’s equations

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Chenxi Guo ◽  
Guillaume Bal
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Two Dimensional ◽  
Complex Valued ◽  
Anisotropic Tensor

Abstract This paper concerns the imaging of a complex-valued anisotropic tensor

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