Structure and dynamical properties of two-dimensional dusty plasmas on one-dimensional periodic substrates

2021 ◽  
Vol 28 (4) ◽  
pp. 040501
Author(s):  
Yan Feng ◽  
Wei Li ◽  
C. Reichhardt ◽  
C. J. O. Reichhardt ◽  
M. S. Murillo
Keyword(s):  
Dusty Plasmas ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dynamical Properties

scholarly journals Continuous and discontinuous transitions in the depinning of two-dimensional dusty plasmas on a one-dimensional periodic substrate

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
L. Gu ◽  
W. Li ◽  
C. Reichhardt ◽  
C. J. O. Reichhardt ◽  
M. S. Murillo ◽  
...  
Keyword(s):  
Dusty Plasmas ◽  
Two Dimensional ◽  
One Dimensional

SOME PECULIAR PROPERTIES OF THE DARWIN’S LAGRANGIAN

1995 ◽  
Vol 09 (23) ◽  
pp. 3069-3083 ◽  
Author(s):  
I.P. PAVLOTSKY ◽  
M. STRIANESE
Keyword(s):  
Phase Space ◽  
Dimensional Case ◽  
Minimal Distance ◽  
Rectilinear Motion ◽  
Two Dimensional ◽  
Singular Surfaces ◽  
One Dimensional ◽  
Local Singularity ◽  
Dynamical Properties

In the post-Galilean approximation the Lagrangians are singular on a submanifold of the phase space. It is a local singularity, which differs from the ones considered by Dirac. The dynamical properties are essentially peculiar on the studied singular surfaces. In the preceding publications,1,2,3 two models of singular relativistic Lagrangians and the rectilinear motion of two electrons, determined by Darwin’s Lagrangian, were examined. In the present paper we study the peculiar dynamical properties of the two-dimensional Darwin’s Lagrangian. In particular, it is shown that the minimal distance between two electrons (the so called “radius of electron”) appears in the two-dimensional motion as well as in one-dimensional case. Some new peculiar properties are discovered.

scholarly journals Structures and diffusion of two-dimensional dusty plasmas on one-dimensional periodic substrates

2018 ◽  
Vol 98 (6) ◽  
Author(s):  
Kang Wang ◽  
Wei Li ◽  
Dong Huang ◽  
C. Reichhardt ◽  
C. J. O. Reichhardt ◽  
...  
Keyword(s):  
Dusty Plasmas ◽  
Two Dimensional ◽  
One Dimensional ◽  
And Diffusion

scholarly journals On the notion of the dimension with respect to a dynamical system

1984 ◽  
Vol 4 (3) ◽  
pp. 405-420 ◽  
Author(s):  
Ya. B. Pesin
Keyword(s):  
Dynamical System ◽  
Hausdorff Dimension ◽  
Invariant Sets ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Common Features ◽  
Dynamical Properties ◽  
The One ◽  
Hyperbolic Sets

AbstractFor the invariant sets of dynamical systems a new notion of dimension-the so-called dimension with respect to a dynamical system-is introduced. It has some common features with the general topological notion of the dimension, but it also reflects the dynamical properties of the system. In the one-dimensional case it coincides with the Hausdorff dimension. For multi-dimensional hyperbolic sets formulae for the calculation of our dimension are obtained. These results are generalizations of Manning's results obtained by him for the Hausdorff dimension in the two-dimensional case.

ON BEHAVIORS OF TWO-DIMENSIONAL ENDOMORPHISMS: ROLE OF THE CRITICAL CURVES

1993 ◽  
Vol 03 (01) ◽  
pp. 187-194 ◽  
Author(s):  
CHRISTIAN MIRA ◽  
TONY NARAYANINSAMY
Keyword(s):  
Critical Points ◽  
Two Dimensional ◽  
One Dimensional ◽  
Critical Curves ◽  
Dynamical Properties

Critical curves are the natural two-dimensional extension of the notion of critical points in one-dimensional endomorphisms. They play a fundamental role in determining the dynamical properties and their bifurcations. This letter demonstrates such a role for two new behaviors.

ESTIMATING THE DIMENSIONAL CHARACTERISTICS OF TWO-DIMENSIONAL PATTERNS

1995 ◽  
Vol 05 (01) ◽  
pp. 109-121 ◽  
Author(s):  
A.L. ZHELEZNYAK ◽  
L.O. CHUA
Keyword(s):  
Fractal Dimensions ◽  
Computer Experiments ◽  
Two Dimensional ◽  
One Dimensional ◽  
Theoretical Predictions ◽  
The Matrix ◽  
Spatially Extended ◽  
Spatially Extended Systems ◽  
Dynamical Properties ◽  
Generalized Dimensions

Dynamical properties of two-dimensional patterns generated by spatially extended systems can be described via the characteristics of attractors in the matrix phase space of the associated translation (or translational-evolution) dynamical systems. Questions regarding the possibility of estimating the fractal dimensions of two-dimensional patterns from the fractal dimensions of one-dimensional observables scanning the patterns along a chosen path are investigated. The presented proofs state that the generalized dimensions of the scanning observables are lower bounds for estimating the corresponding generalized dimensions of two-dimensional patterns. Spatial field distributions defined as superposition of planar waves and different spatiotemporal patterns produced by cellular neural networks made of Chua’s circuits are studied numerically. The results of computer experiments confirm the theoretical predictions presented in this paper.

scholarly journals Oscillation-like diffusion of two-dimensional liquid dusty plasmas on one-dimensional periodic substrates with varied widths

2020 ◽  
Vol 27 (3) ◽  
pp. 033702 ◽  
Author(s):  
W. Li ◽  
C. Reichhardt ◽  
C. J. O. Reichhardt ◽  
M. S. Murillo ◽  
Yan Feng
Keyword(s):  
Dusty Plasmas ◽  
Two Dimensional ◽  
One Dimensional

scholarly journals Phonon spectra of two-dimensional liquid dusty plasmas on a one-dimensional periodic substrate

2018 ◽  
Vol 98 (6) ◽  
Author(s):  
W. Li ◽  
D. Huang ◽  
K. Wang ◽  
C. Reichhardt ◽  
C. J. O. Reichhardt ◽  
...  
Keyword(s):  
Dusty Plasmas ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phonon Spectra

scholarly journals Depinning dynamics of two-dimensional dusty plasmas on a one-dimensional periodic substrate

2019 ◽  
Vol 100 (3) ◽  
Author(s):  
W. Li ◽  
K. Wang ◽  
C. Reichhardt ◽  
C. J. O. Reichhardt ◽  
M. S. Murillo ◽  
...  
Keyword(s):  
Dusty Plasmas ◽  
Two Dimensional ◽  
One Dimensional

On critical point for two-dimensional holomorphic systems

2016 ◽  
Vol 37 (7) ◽  
pp. 2276-2312
Author(s):  
FRANCISCO VALENZUELA-HENRÍQUEZ
Keyword(s):  
Critical Point ◽  
Complex Manifold ◽  
Invariant Set ◽  
Two Dimensional ◽  
Dominated Splitting ◽  
One Dimensional ◽  
Dynamical Object ◽  
Dynamical Properties

Let $f:M\rightarrow M$ be a biholomorphism on a two-dimensional complex manifold, and let $X\subseteq M$ be a compact $f$-invariant set such that $f|_{X}$ is asymptotically dissipative and without periodic sinks. We introduce a solely dynamical obstruction to dominated splitting, namely critical point. Critical point is a dynamical object and captures many of the dynamical properties of a one-dimensional critical point.

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