scholarly journals Quenched topological boundary modes can persist in a trivial system

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Ching Hua Lee ◽  
Justin C. W. Song
Keyword(s):  
Probability Density ◽  
Power Law ◽  
Localized States ◽  
Topological Phase ◽  
Boundary Mode ◽  
Temporal Boundary ◽  
And Control ◽  
Topological Boundary

AbstractTopological boundary modes can occur at the spatial interface between a topological and gapped trivial phase and exhibit a wavefunction that exponentially decays in the gap. Here we argue that this intuition fails for a temporal boundary between a prequench topological phase that possess topological boundary eigenstates and a postquench gapped trivial phase that does not possess any eigenstates in its gap. In particular, we find that characteristics of states (e.g., probability density) prepared in a topologically non-trivial system can persist long after it is quenched into a gapped trivial phase with spatial profiles that appear frozen over long times postquench. After this near-stationary window, topological boundary mode profiles decay albeit, slowly in a power-law fashion. This behavior highlights the unusual features of nonequilibrium protocols enabling quenches to extend and control localized states of both topological and non-topological origins.

Area and volume quantification of arctic thaw slumps using time-series of digital elevation models generated from radar interferometry

2021 ◽  
Author(s):  
Philipp Bernhard ◽  
Simon Zwieback ◽  
Irena Hajnsek
Keyword(s):  
Probability Density ◽  
Power Law ◽  
Volume Change ◽  
Digital Elevation Models ◽  
Probability Density Functions ◽  
The Arctic ◽  
Density Functions ◽  
Digital Elevation ◽  
Beta Coefficient ◽  
Area And Volume

<p>Vast areas of the Arctic host ice-rich permafrost, which is becoming increasingly vulnerable to terrain-altering thermokarst in a warming climate. Among the most rapid and dramatic changes are retrogressive thaw slumps. These slumps evolve by a retreat of the slump headwall during the summer months, making their change visible by comparing digital elevation models over time. In this study we use digital elevation models generated from single-pass radar TanDEM-X observations to derive volume and area change rates for retrogressive thaw slumps. At least three observations in the timespan from 2011 to 2017 are available with a spatial resolution of about 12 meter and a height sensitivity of about 0.5-2 meter. Our study regions include regions in Northern Canada (Peel Plateau/Richardson Mountains, Mackenzie River Delta Uplands, Ellesmere Island), Alaska (Noatak Valley) and Siberia (Yamal, Gydan, Taymyr, Chukotka) covering an area of 220.000 km<sup>2</sup> with a total number of 1853 thaw slumps.</p><p>In this presentation we will focus on the area and volume change rate probability density functions of the mapped thaw slumps in these study areas. For landslides in temperate climate zones the area and volume change probability density function typically follow a distribution that can be characterized by three quantities: A rollover point defined as the peak in the distribution, a cutoff-point indicating the transition to a power law scaling for large landslides and the exponential beta coefficient of this power law. Here we will show that thaw slumps across the arctic follow indeed such a distribution and that the obtained values for the rollover, cutoff and beta coefficient can be used to distinguish between regions. Furthermore we will elaborate on possible reason why arctic thaw slumps can be described by such probability density functions as well as analyzing the differences between regions. This characterization can be useful to further improve our understanding of thaw slump initiation, the investigation of the drivers of their evolution as well as for modeling future thaw slump activity.</p>

Invariants of Chaotic Attractor in a Nonlinearly Damped System

1998 ◽  
Vol 65 (4) ◽  
pp. 875-879 ◽  
Author(s):  
B. Ravindra ◽  
P. Hagedorn
Keyword(s):  
Power Law ◽  
Chaotic Attractor ◽  
Correlation Dimension ◽  
Ml Estimation ◽  
State Space Reconstruction ◽  
Damped System ◽  
Building Models ◽  
Prediction And Control ◽  
And Control

The characterization of a chaotic attractor in a driven, Duffing-Holmes oscillator with power-law damping is considered. State space reconstruction of the time series of the attractor is carried out to investigate its structure. The invariants associated with the attractor such as correlation dimension and entropy are computed. Also the maximum-likelihood (ML) estimation of dimension and entropy are carried out. The use of obtained invariants in building models for prediction and control using power-law dampers is discussed.

GENERATION AND CONTROL ANALYSIS OF A MULTISTATE INTERMITTENT SYSTEM

2010 ◽  
Vol 20 (11) ◽  
pp. 3663-3671 ◽  
Author(s):  
GUANGMING XIE ◽  
YIYANG YU
Keyword(s):  
Nonlinear System ◽  
Power Law ◽  
Complex Dynamics ◽  
Invariant Subspaces ◽  
Control Analysis ◽  
Power Law Distribution ◽  
System Parameters ◽  
And Control

In this paper, a Rössler-driving multistate intermittency is generated by a nonlinear system that contains controllable invariant subspaces. Intermittency-induced multiscroll attractor is found, and moreover, the control analysis is discussed, such as the number of attractors and the distance between laminar states can be easily adjusted by tuning some system parameters. The statistic behavior and power law distribution are also discussed, which reveal the regularities in the complex dynamics.

"SPIRAL WAVE–TRAVELING CLUSTERING" INTERMITTENCY AND 1/f-NOISE IN A 2D COUPLED MAP LATTICE

1999 ◽  
Vol 09 (05) ◽  
pp. 929-937 ◽  
Author(s):  
MARK A. PUSTOVOIT ◽  
VALERY I. SBITNEV
Keyword(s):  
Probability Density ◽  
Exponential Decay ◽  
Power Law ◽  
Strange Attractor ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
The Self ◽  
Saddle Node Bifurcation ◽  
Self Organized

Intermittency of checkerboard spiral waves and traveling clusterings originating from sudden shrinking of the strange attractor of the 2D CML in the neighborhood of the saddle-node bifurcation boundary is found. A power-law probability density for lifetimes in the spiral wave (laminar) phase is observed, while in the checkerboard clusterings (bursting) phase the above quantity exhibits an exponential decay. This difference can be interpreted through the self-organized behavior of the spiral waves, and the passive relaxation of the disordered checkerboard clusterings.

Random coefficient autoregression, regime switching and long memory

2003 ◽  
Vol 35 (03) ◽  
pp. 737-754 ◽  
Author(s):  
Remigijus Leipus ◽  
Donatas Surgailis
Keyword(s):  
Probability Density ◽  
Power Law ◽  
Renewal Process ◽  
Long Memory ◽  
Regime Switching ◽  
Covariance Function ◽  
Random Coefficient ◽  
Levy Process ◽  
Partial Sums ◽  
Stable Lévy Process

We discuss long-memory properties and the partial sums process of the AR(1) process {X t , t ∈ 𝕫} with random coefficient {a t , t ∈ 𝕫} taking independent values A j ∈ [0,1] on consecutive intervals of a stationary renewal process with a power-law interrenewal distribution. In the case when the distribution of generic A j has either an atom at the point a=1 or a beta-type probability density in a neighborhood of a=1, we show that the covariance function of {X t } decays hyperbolically with exponent between 0 and 1, and that a suitably normalized partial sums process of {X t } weakly converges to a stable Lévy process.

Complex Unconstrained Three-Dimensional Hand Movement and Constant Equi-Affine Speed

2009 ◽  
Vol 101 (2) ◽  
pp. 1002-1015 ◽  
Author(s):  
Uri Maoz ◽  
Alain Berthoz ◽  
Tamar Flash
Keyword(s):  
Power Law ◽  
Hand Movement ◽  
Three Dimensional ◽  
Hand Movements ◽  
Human Hand ◽  
Local Geometry ◽  
Planning And Control ◽  
Human Movements ◽  
And Control ◽  
Geometry And Kinematics

One long-established simplifying principle behind the large repertoire and high versatility of human hand movements is the two-thirds power law—an empirical law stating a relationship between local geometry and kinematics of human hand trajectories during planar curved movements. It was further generalized not only to various types of human movements, but also to motion perception and prediction, although it was unsuccessful in explaining unconstrained three-dimensional (3D) movements. Recently, movement obeying the power law was proved to be equivalent to moving with constant planar equi-affine speed. Generalizing such motion to 3D space—i.e., to movement at constant spatial equi-affine speed—predicts the emergence of a new power law, whose utility for describing spatial scribbling movements we have previously demonstrated. In this empirical investigation of the new power law, subjects repetitively traced six different 3D geometrical shapes with their hand. We show that the 3D power law explains the data consistently better than both the two-thirds power law and an additional power law that was previously suggested for spatial hand movements. We also found small yet systematic modifications of the power-law's exponents across the various shapes, which further scrutiny suggested to be correlated with global geometric factors of the traced shape. Nevertheless, averaging over all subjects and shapes, the power-law exponents are generally in accordance with constant spatial equi-affine speed. Taken together, our findings provide evidence for the potential role of non-Euclidean geometry in motion planning and control. Moreover, these results seem to imply a relationship between geometry and kinematics that is more complex than the simple local one stipulated by the two-thirds power law and similar models.

scholarly journals Statistical Analysis of Acoustic Emission in Uniaxial Compression of Tectonic and Non-Tectonic Coal

2020 ◽  
Vol 10 (10) ◽  
pp. 3555 ◽  
Author(s):  
Rong Liu ◽  
Yi He ◽  
Yunfeng Zhao ◽  
Xiang Jiang ◽  
Song Ren
Keyword(s):  
Acoustic Emission ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Uniaxial Compression ◽  
Power Law ◽  
Waiting Time ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Tectonic Coal

Tectonic coal has become an important research topic for preventing coal mine disasters and for exploring and developing coal-bed methane resources. To investigate the mechanical and acoustic properties of tectonic coal, we conducted a uniaxial compression test for tectonic and non-tectonic coal, and acoustic emission (AE) signals have been simultaneous captured in the compression process. The AE energy and waiting time of events have been studied statistically. The results show that the probability density function of AE energy follows the power law distribution well, and indicates that the AE of non-tectonic coal is mainly generated from the fracture source, while the probability density function distribution of tectonic coal is the mixing result of fracture and friction effects. Only the waiting time distribution of non-tectonic coal follows the typical brittle fracture’s double power law behavior. The waiting time distribution of tectonic coal shows the single power law with a smaller exponent value, which is associated with the granular microstructure of tectonic coal. The distribution of aftershock and Båth’s law are not sensitive to microstructure, and are identical for non-tectonic and tectonic coal. At last, the correlation dimension results for the spatial distribution of AE hypocenters indicated that the rough continuous decrease in multifractal dimension might be a precursor to devastating destruction.

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