Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Some dynamical properties for a bouncer model—a classical particle of massmfalling in the presence of a constant gravitational fieldgand hitting elastically a periodically moving wall—in the presence of drag force that is assumed to be proportional to the particle's velocity are studied. The dynamics of the model is described in terms of a two-dimensional nonlinear mapping obtained via solution of the second Newton's law of motion. We characterize the behavior of the average velocity of the particle as function of the control parameters as well as the time. Our results show that the average velocity starts growing at first and then bends towards a regime of constant value, thus confirming that the introduction of drag force is a sufficient condition to suppress Fermi acceleration in the model.

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Scaling Properties of a Hybrid Fermi-Ulam-Bouncer Model

Mathematical Problems in Engineering ◽

10.1155/2009/213857 ◽

2009 ◽

Vol 2009 ◽

pp. 1-13 ◽

Cited By ~ 6

Author(s):

Diego F. M. Oliveira ◽

Rafael A. Bizão ◽

Edson D. Leonel

Keyword(s):

Critical Exponents ◽

Average Velocity ◽

Chaotic Regime ◽

Two Dimensional ◽

Scaling Properties ◽

One Dimensional ◽

Dynamical Properties ◽

Scaling Invariant ◽

Area Preserving

Some dynamical properties for a one-dimensional hybrid Fermi-Ulam-bouncer model are studied under the framework of scaling description. The model is described by using a two-dimensional nonlinear area preserving mapping. Our results show that the chaotic regime below the lowest energy invariant spanning curve is scaling invariant and the obtained critical exponents are used to find a universal plot for the second momenta of the average velocity.

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Laboratory measurements of the drag force on a family of two-dimensional ice keel models in a two-layer flow

International Journal of Multiphase Flow ◽

10.1016/s0301-9322(97)88458-3 ◽

1996 ◽

Vol 22 ◽

pp. 133

Author(s):

H Pite

Keyword(s):

Drag Force ◽

Two Dimensional ◽

Laboratory Measurements ◽

Layer Flow

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SCALING INVARIANCE IN A TIME-DEPENDENT ELLIPTICAL BILLIARD

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127412502070 ◽

2012 ◽

Vol 22 (09) ◽

pp. 1250207 ◽

Cited By ~ 5

Author(s):

DIEGO F. M. OLIVEIRA ◽

MARKO ROBNIK

Keyword(s):

Integrable System ◽

Average Velocity ◽

Moving Boundary ◽

Time Dependent ◽

Scaling Invariance ◽

Energy Growth ◽

Dynamical Properties ◽

Scaling Arguments

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although the static elliptical billiard is an integrable system, after introducing time-dependent perturbation on the boundary the unlimited energy growth is observed. The behavior of the average velocity is described using scaling arguments.

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An Adaptive Chaos Synchronization with Controller and Secure Communication

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.401-403.1657 ◽

2013 ◽

Vol 401-403 ◽

pp. 1657-1660

Author(s):

Bin Zhou ◽

Xiang Wang ◽

Yu Gao ◽

Shao Cheng Qu

Keyword(s):

Adaptive Control ◽

Lyapunov Stability ◽

Stability Theory ◽

Secure Communication ◽

Chaos Synchronization ◽

Lyapunov Stability Theory ◽

Adaptive Controller ◽

Adaptive Synchronization ◽

Sufficient Condition ◽

Control Parameters

An adaptive controller with adaptive rate is presented to synchronize two chaos systems and to apply to secure communication. Based on Lyapunov stability theory, a sufficient condition and adaptive control parameters are obtained. Finally, the simulation with synchronization and secure communication is given to show the effectiveness of the proposed method. Keywords: adaptive; synchronization; observer; controller.

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Design of an Observer-Based Repetitive Control System to Reject Periodic Disturbance

Journal of Circuits System and Computers ◽

10.1142/s0218126616500614 ◽

2016 ◽

Vol 25 (06) ◽

pp. 1650061 ◽

Cited By ~ 1

Author(s):

Zhen Shao ◽

Zhengrong Xiang

Keyword(s):

Control System ◽

Disturbance Rejection ◽

Lyapunov Functional ◽

Repetitive Control ◽

Sufficient Condition ◽

Two Dimensional ◽

Periodic Disturbance ◽

Repetitive Learning ◽

The Stability ◽

2D Model

This paper concerns the design of an observer-based repetitive control system (RCS) to improve the periodic disturbance rejection performance. The periodic disturbance is estimated by a repetitive learning based estimator (RLE) and rejected by incorporation of the estimation into a repetitive control (RC) input. Firstly, the configuration of the observer-based RCS with the RLE is described. Then, a continuous–discrete two-dimensional (2D) model is built to describe the RCS. By choosing an appropriate Lyapunov functional, a sufficient condition is proposed to guarantee the stability of the RCS. Finally, a numerical example is given to verify the effectiveness of the proposed method.

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Dynamical properties of ring dark soliton in quasi-two dimensional Bose-Einstein condensates

Acta Physica Sinica ◽

10.7498/aps.57.6786 ◽

2008 ◽

Vol 57 (11) ◽

pp. 6786

Author(s):

Zhang Wei-Xi ◽

Wang Deng-Long ◽

Ding Jian-Wen

Keyword(s):

Dark Soliton ◽

Two Dimensional ◽

Dynamical Properties ◽

Bose Einstein

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Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

Mathematical Problems in Engineering ◽

10.1155/2009/367921 ◽

2009 ◽

Vol 2009 ◽

pp. 1-22 ◽

Cited By ~ 4

Author(s):

Edson D. Leonel

Keyword(s):

Phase Transition ◽

Critical Exponents ◽

Scaling Laws ◽

Scaling Function ◽

Initial Conditions ◽

Invariant Tori ◽

Dynamical Variable ◽

Two Dimensional ◽

Control Parameters ◽

Average Value

A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map.

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Conditions for the Separability of Objects in Two-Dimensional Velocity Fields

Canadian Mathematical Bulletin ◽

10.4153/cmb-1992-063-1 ◽

1992 ◽

Vol 35 (4) ◽

pp. 484-491

Author(s):

Stephan Foldes

Keyword(s):

Velocity Field ◽

Directed Graph ◽

Velocity Fields ◽

Sufficient Condition ◽

Two Dimensional ◽

Jordan Curves ◽

Directed Cycles

AbstractWe consider the directed graph representing the obstruction relation between objects moving along the streamlines of a two-dimensional velocity field. A collection of objects is sequentially separable if and only if the corresponding graph has no directed cycles. A sufficient condition for this is the permeability of closed Jordan curves.

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Ab-initio study of dynamical properties of two dimensional MoS2 under strain

AIP Advances ◽

10.1063/1.4932974 ◽

2015 ◽

Vol 5 (10) ◽

pp. 107103 ◽

Cited By ~ 14

Author(s):

Himadri Soni ◽

Prafulla K. Jha

Keyword(s):

Ab Initio ◽

Two Dimensional ◽

Ab Initio Study ◽

Dynamical Properties

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A Method to Double the Extension Ability of Radial Jet Drilling Technology

Journal of Energy Resources Technology ◽

10.1115/1.4039977 ◽

2018 ◽

Vol 140 (9) ◽

Cited By ~ 6

Author(s):

Li Jingbin ◽

Zhang Guangqing ◽

Li Gensheng ◽

Huang Zhongwei ◽

Li Weichang

Keyword(s):

Drag Force ◽

Average Velocity ◽

Oil And Gas ◽

Damage Zone ◽

Force Model ◽

Gas Recovery ◽

Drainage Radius ◽

Velocity Flow ◽

Critical Issues ◽

Drilling Technology

Radial jet drilling (RJD) technology is an effective method to enhance oil and gas recovery by penetrating the near-wellbore damage zone, and increasing the drainage radius greatly. Recently, it is identified as a potential technology to develop the geothermal energy. But the extension ability, one of the most critical issues of the RJD, is limited. Because only high pressure flexible hose (HPFH), which is hard to be fed in and subjected to greater resistance by the diverter, can be used as the drill stem to turn from vertical to horizontal in the casing. In this paper, an innovative method to feed in the HPFH by the drag force generated by high velocity flow in narrow annulus is proposed. The drag force model is built, validated, and modified by theoretical and experimental ways. Results show that the resulting drag force, which is equivalent to the self-propelled force, can easily achieve and feed in the HPFH. There is a power law relationship between the drag force and the average velocity; the drag force increases linearly with the length of the narrow annulus. Higher average velocity and 1–1.5 m annulus length are recommended. According to force analysis, the extension ability of the RJD can be doubled theoretically by this method. The results of this paper will greatly promote the development of RJD technology.

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