scholarly journals Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 746 ◽  
Author(s):  
Longwen Zhou
Keyword(s):  
Open Systems ◽  
Symmetry Class ◽  
Open Boundary ◽  
Topological Invariants ◽  
Open Boundary Condition ◽  
Periodically Driven ◽  
New Type ◽  
The Mean ◽  
Time Periodic ◽  
Topological Matter

Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants ( w 0 , w π ) ∈ 2 Z × 2 Z . Under the open boundary condition, these invariants further predict the number of zero- and π -quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.

INFLUENCE OF INFORMATION ON CROWD DISPERSION PROCESS

2009 ◽  
Vol 20 (07) ◽  
pp. 1001-1010 ◽  
Author(s):  
H. TIAN ◽  
Y. XUE ◽  
Y.-F. WEI
Keyword(s):  
Boundary Condition ◽  
Lattice Gas ◽  
Critical Density ◽  
Square Lattice ◽  
Open Boundary ◽  
Open Boundary Condition ◽  
Mean Velocity ◽  
Dispersion Process ◽  
Random Walkers ◽  
The Mean

The influence of information on the pedestrian in crowd dispersion process is investigated under the open boundary condition on the square lattice by the use of the lattice gas model of biased random walkers without the back step. It is found that the jamming phenomenon occurs when the total entrance density is small in spite of influence of information. The mean velocity 〈v〉 ped of the walkers moving remains a constant via a small fluctuation for the small total entrance density, but for the large total entrance density, the 〈v〉 ped increases from 0 to 1. The mean velocity 〈v〉 inf of information spreading increases from 0 to 1, and then decreases to 0. The critical density decreases with increasing the size W of the system. When the size of the system is small, the platform appears because of asymmetry in propagation of information.

scholarly journals Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Thomas Eiter ◽  
Mads Kyed
Keyword(s):  
Rigid Body ◽  
Sobolev Spaces ◽  
Periodic Motion ◽  
Viscous Incompressible Fluid ◽  
Body Motion ◽  
Translational Velocity ◽  
Ill Posed ◽  
Homogeneous Sobolev Spaces ◽  
The Mean ◽  
Time Periodic

AbstractThe equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

Stability and Stabilization for Discrete System With Probabilistic Nonlinearities

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Xia Zhao ◽  
Engang Tian
Keyword(s):  
Sufficient Conditions ◽  
Discrete Systems ◽  
System Model ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Mean Square Stability ◽  
New Type ◽  
Stability And Stabilization ◽  
The Mean ◽  
Varying Delay

This paper investigates stability and stabilization of discrete systems with probabilistic nonlinearities and time-varying delay. New characters of the nonlinearities, the probability of the nonlinearities happening between different bounds, are used to build new type of system model, which can help us make a full use of the inner variation information of the nonlinearities. With the help of the new characters, new system model is proposed. Then, sufficient conditions for the mean square stability of the system can be obtained by using the Lyapunov functional approach and linear matrix inequalities technique. An example is proposed to illustrate the efficiency of the proposed method.

ANALYSIS OF THE INFLUENCE OF LANE CHANGING ON TRAFFIC-FLOW DYNAMICS BASED ON THE CELLULAR AUTOMATON MODEL

2011 ◽  
Vol 22 (03) ◽  
pp. 271-281 ◽  
Author(s):  
SHINJI KUKIDA ◽  
JUN TANIMOTO ◽  
AYA HAGISHIMA
Keyword(s):  
Boundary Condition ◽  
Cellular Automaton ◽  
Numerical Simulations ◽  
Traffic Flow ◽  
Flow Dynamics ◽  
Open Boundary ◽  
Open Boundary Condition ◽  
Lane Changing ◽  
Basic Characteristics ◽  
Conventional Models

Many cellular automaton models (CA models) have been applied to analyze traffic flow. When analyzing multilane traffic flow, it is important how we define lane-changing rules. However, conventional models have used simple lane-changing rules that are dependent only on the distance from neighboring vehicles. We propose a new lane-changing rule considering velocity differences with neighboring vehicles; in addition, we embed the rules into a variant of the Nagel–Schreckenberg (NaSch) model, called the S-NFS model, by considering an open boundary condition. Using numerical simulations, we clarify the basic characteristics resulting from different assumptions with respect to lane changing.

A New Type of One-Bit Digital Correlator

1980 ◽  
Vol 4 (1) ◽  
pp. 21-23
Author(s):  
T. W. Cole
Keyword(s):  
Ordered Set ◽  
New Type ◽  
The Mean ◽  
Digital Correlator

Given an ordered set of samples {ai} of some function, then the autocorrelation of that function is the mean lagged product of these samples.

scholarly journals Measuring Chern numbers in Hofstadter strips

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Samuel Mugel ◽  
Alexandre Dauphin ◽  
Pietro Massignan ◽  
Leticia Tarruell ◽  
Maciej Lewenstein ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary Conditions ◽  
Chern Number ◽  
Open Boundary ◽  
Topological Invariants ◽  
Transverse Displacement ◽  
Open Boundary Conditions ◽  
Open Questions ◽  
Chern Numbers ◽  
Spatial Dimensions

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wave packet exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.

scholarly journals Improvements on Learning Kernel Extended Dictionary for Face Recognition

2020 ◽  
Vol 34 (4) ◽  
pp. 387-394
Author(s):  
Soodabeh Amanzadeh ◽  
Yahya Forghani ◽  
Javad Mahdavi Chabok
Keyword(s):  
Sparse Representation ◽  
Face Image ◽  
Collaborative Representation ◽  
Training Images ◽  
Input Face ◽  
Proposed Model ◽  
Eigen Values ◽  
New Type ◽  
The Mean ◽  
Better Than

Kernel extended dictionary learning model (KED) is a new type of Sparse Representation for Classification (SRC), which represents the input face image as a linear combination of dictionary set and extended dictionary set to determine the input face image class label. Extended dictionary is created based on the differences between the occluded images and non-occluded training images. There are four defaults to make about KED: (1) Similar weights are assigned to the principle components of occlusion variations in KED model, while the principle components of the occlusion variations have different weights, which are proportional to the principle components Eigen-values. (2) Reconstruction of an occluded image is not possible by combining only non-occluded images and the principle components (or the directions) of occlusion variations, but it requires the mean of occlusion variations. (3) The importance and capability of main dictionary and extended dictionary in reconstructing the input face image is not the same, necessarily. (4) KED Runtime is high. To address these problems or challenges, a novel mathematical model is proposed in this paper. In the proposed model, different weights are assigned to the principle components of occlusion variations; different weights are assigned to the main dictionary and extended dictionary; an occluded image is reconstructed by non-occluded images and the principle components of occlusion variations, and also the mean of occlusion variations; and collaborative representation is used instead of sparse representation to enhance the runtime. Experimental results on CAS-PEAL subsets showed that the runtime and accuracy of the proposed model is about 1% better than that of KED.

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